Cut up a critter and brown it, then add water, beer or stock and simmer it with onion, celery and carrots, garlic, and whatever seasonings you like (sage, oregano and bay for chicken and rabbit). Take the meat out, and either strain out the veggies or puree them, then cook the liquid down about halfway. Slow-brown a roux using flour and the skimmed fat or some butter, stir it into the simmering liquid, and when it starts thickening add half and half until you get the consistency of gravy you like. Put the meat back in, bring the gravy back up to the simmering point, and add salt, pepper and some lemon juice.
Serve with big buttermilk biscuits, lumpy mashed potatoes drowned in the gravy, corn on the cob, carrots glazed in brown sugar with a little ginger and black pepper, and finish off with sweet-potato pie.