Researching early medieval food presents one huge obstacle: there are virtually no period sources on the subject (late medieval food has a number of cookbooks to its credit, not to mention scattered accounts, medical texts, etc). So, aside from picking through histories, hagiographies, church canons, legal codes, etc. for the precious shards of information, one inevitably turns to archaeology, both in general and in its more specialized forms.
I've been doing this for a while, but it only recently occurred to me that the ways in which meat was butchered provide some very useful hints on how it was cooked. There's no lack of animal bones in archaeological finds, so this should be a promising avenue. And in fact it is; but unfortunately most accounts of such finds don't say much about the details of butchery, either because for much of the period this would have been very simplistic or because in many cases the scholars in question simply don't feel competent to comment on these in any depth.
The one big exception is for Gallo-Roman butchery. This may well be because the Romans (including the ones in Gaul we now call "Gallo-Romans") had professional butchers and so a scholar has more to, as it were, sink her or his teeth into in this area. It's also true that cities tend to offer more concentrated finds and cities played a bigger part in Gallo-Roman life than in Frankish life. At the same time, such information is not in the least uninteresting for the early medieval period, if only because the Gallo-Roman culture survived in the south for at least two centuries, but also because to the degree that any sophisticated techniques were known (as by the rare household butchers mentioned in later texts) these probably were based on those surviving from the professional Roman butchers.
Better yet, such studies sometimes highlight the difference between urban and rural butchery. The latter was probably not too different from what the Germans were doing before contact with the Romans and so gives at least tentative insight into what was going on in the more Frankish regions. In a nutshell, butchers in the cities tended to be professionals who served a large, varied clientele that ate meat as individuals or in small family groups and so the meat was cut up into smaller and more varied pieces, while in the country non-specialized personnel prepared larger cuts of meat - or just whole animals - for groups which often ate collectively and so could take care of dividing up the animal while eating, not before cooking. Also, the Romans largely used cleavers whereas the preferred instrument in the countryside (and among the Germans) was the knife; in practice, as Roman influence spread, use of these can be found in varying combinations.
Butchering is a complex craft and one probably has to be a trained butcher oneself to understand all the nuances of cuts laid out in one of these papers. But to simplify somewhat, a few things can be said about the more professional Roman butchering. Spines might be removed entirely (today they are often sliced in half), after evisceration and removal of the ribs (which sometimes were cut separately and sometimes left attached to a portion of the spine). Doing this left a lot of meat free for what today would be steaks; in French terms, filets, contre-filets, rumsteaks, etc. It is not clear however that anyone thought to cook or select these separately until the late medieval period (where one first reads of "slices"- lesches - of meat and then, in England, of actual "steykes"). Nothing of the sort is mentioned either in the two great Roman culinary sources (pseudo-Apicius and Anthimus) nor in literature - which certainly does not prove definitively that the concept did not exist, but reduces the likelihood. Since a lot of cuts (including the ribs) were often deboned, a fair amount of boneless meat seems to have been available to the urban consumer, but given the popularity of boiling what we consider filet mignon may have ended up in a stewpot rather than on a grill (even if the Romans also made ample use of those).
The body was often cut (even later) into front and hind 'quarters', which could in fact include collars, ribs, etc as well; in the countryside such quartering may have been the main butchering operation. There was also some difference between animals, if only because cattle, for instance, were too big to be treated in the same way as sheep or pigs. Most seems to be known in the documentation about pigs, the preferred food of the well-off, and just about everything on them was used - even the blood served for blood sausage. It is unclear if cattle viscera were kept or used but it seems clear that those of pigs were (for tripe, etc).
The brains and tongues of all the major animals were eaten, as shown by opening of skulls and complex cuts around the jaws. Anthimus mentions kidneys (disapprovingly) and probably other offal, whose removal would not leave such marks, was eaten as well.
In the cities, long bones were often cut up into smaller pieces, either by the butcher or the homemaker, to be used in stews and soups. Vertebrae are sometimes found cut up and probably were used in soup as well. It should be noted too that marrow was long popular and domestic bones are sometimes found shattered to retrieve it.
In general, the smaller cuts seem to have been intended for boiling of some sort, even if some animals were roasted on spits and ribs may have been grilled or even baked in the small ovens found in some Roman kitchens (which typically centered around a grill set on a larger workspace). Some smaller animals, however, (like sheep) may also have been sold whole to be roasted (as in today's mechouis).
Remains from the countryside tend to be far less segmented and in fact sometimes represent whole animals. Again, any division, or simple removal of the meat, could then have occurred after broiling or boiling.
Those are some of the highlights of what can be deduced from signs of butchery on surviving bones. For a closer look: