In a large bowl, combine the orange and lime juice, garlic, salt, and pepper. Add the meat and toss to coat. Let marinate for a half hour to 24 hours (if more than an hour, cover and refrigerate). Bring to room temperature before cooking.
Heat oil in a large and extended casserole over high heat. Once hot, cooking in batches if necessary to not overcrowd the pan, add the meat and brown for 4 to 5 minutes, flipping as it does. Remove browned meat with a slotted spoon or spider.
Once you have browned all the meat, return it to the casserole and add enough water to barely cover it. Add the bay leaves and stir. Bring to a rolling boil, then reduce the heat to medium low, cover, and cook for a couple hours, until the meat is completely cooked through and very tender. If there is still liquid in the casserole, continue cooking uncovered until it has cooked off.
Place the meat on a chopping board and chop into small pieces, then return it to the casserole and cover so it will remain hot.
Serve on a plate covered with warm corn tortillas, along with Mixed Chile Salsa Verde and onion and cilantro on the side for people to add to taste.