Preheat oven to 350° F. Cut pork shoulder into five or six large chunks. Heat olive oil and butter in a large Dutch oven, over medium-high setting. Working in batches, sear the pork chunks on all sides until they have a light golden-brown crust. Remove pork and set aside.
Reduce heat to medium and add onion, celery, and carrot. Sweat the mirepoix for about five minutes until soft. Add garlic and cook for another minute. Stir in salt and pepper.
Stir in the tomato paste and cook for a couple of minutes until it starts to brown slightly. Then, sprinkle the flour in the pan and cook it for a couple of minutes as well. Add the red wine and cook to reduce slightly. Return the pork chunks to the Dutch oven.
Add enough beef broth until it reaches the top of the pork but does not cover it. Add parsley and bay leaves, cover the Dutch oven and place in oven for three hours or until fork tender. Allow the meat to rest for five minutes and then serve.
Discard parsley and bay leaves before serving.
If you're not a fan of pork, try an inexpensive cut of beef in this recipe instead. Braising takes tough meat and tenderizes until it's soft and delicious!