Using a sharp knife, trim any excess fat off the meat. Cut it into one-inch cubes.
In a Dutch oven, season meat with salt, pepper, bay leaves, and garlic cloves. Pop the lid on and bake at 250°F for 4 hours if using pork and for 6 hours if using beef.
In the last 30 or so minutes of cooking, turn your attention to prepping the jars for canning. To sterilize the jars, wash them thoroughly with soap and hot water. Place them in the oven next to the Dutch oven for about 15 minutes, or until they're completely dry. Remove the Dutch oven and jars from the oven. Carefully fill each jar with the meat mixture.
While the meat is still hot, use an oven mitt or kitchen towel to protect your hands and close all lids really tight. To seal the jars, flip them upside down for several hours.
Store tushonka in the refrigerator for up to three months. Enjoy with toasted bread or added to your favorite pasta or grain dishes!