Step 1Heat the oven to 275 degrees. Season the pork with salt and black pepper and lightly dredge in flour (if using butt, cut into 3-inch cubes). In a hot skillet, sear the pork pieces in 1 tablespoon olive oil until light brown on all sides and reserve.
Step 2In a large ovenproof cast-iron casserole or saucepan, saute the carrots, onion, celery, bacon and tomato paste in olive oil until the onions begin to turn translucent, about 4 minutes. Add both beers and bring to a boil. Add the veal stock and bring to a simmer.
Step 3Remove from the heat. Add the bay leaves, thyme, vinegar and garlic. Add the pork pieces and cover loosely so that steam will escape and the liquid will reduce while cooking (one technique is to cover the pan with a piece of parchment paper with a vent cut into it). Bake for 3 hours.
Step 4Remove the pork and bacon pieces and reserve (pork should be falling-apart tender). Strain the remaining liquid (there should be about 1 cup) through a fine-mesh sieve. If you have more, reduce the sauce over medium heat until you have 1cup. Cool. Everything up to this point can be done 1 day before serving.
Step 5Before serving, bring the sauce to a slow boil and reduce by one-third. Add the honey and salt and pepper to taste to the reduced sauce. The sauce should coat a spoon.
Step 6Add the reserved pork and bacon pieces to the sauce and reheat for about 7 to 8 minutes over low heat, covered.
Step 7Add the butter and allow it to incorporate in the sauce by swirling the pan just before serving. Serve with wilted greens such as chard, kale, escarole or Tuscan cabbage as well as mashed potatoes or creamy polenta.