From the Goodman of Paris, a late fourteenth-century book of instructions written by a Parisian burgher for his young wife, here are a couple of miscellaneous delicacies.
Hedgehog should have its throat cut, be singed and gutted, then trussed like a pullet, then pressed in a towel until very dry; and then roast it and eat with cameline sauce, or in pastry with wild duck sauce. Note that if the hedgehog refuses to unroll, put it in hot water, and then it will straighten itself.
Squirrels are singed, gutted, trussed like rabbits, roasted or put in pastry: eat with cameline sauce or in pastry with wild duck sauce.
Another one, from the Liber Cure Cocorum, written in England around 1430:
Stewed pigeons. Take pigeons and hew them in small morsels. Put them in an earthen pot. Take peeled garlic and herbs anon. Chop them up small before you do anything else. Put them in your pot and don't leave out the good broth with white grease. Add powder and good verjuice. Colour it with saffron and some salt. Put all these things in your pot and you shall stew your pigeons.
The pigeons probably weren't caught on the street. Medieval people often kept domestic pigeons in cotes.
On the other hand, what to make of this recipe? (Warning: click at your own peril!)