Prepare: Position oven rack in lower half of oven, and preheat to 300 F. Check that all ingredients are measured, prepared, and ready to go.
Cut Pork: Pat pork dry with paper towels. Cut meat into roughly 1-inch chunks or smaller, trimming off excess fat. About 1/2 pound of fat is typically removed, with 2.5 pounds of lean meat remaining.
Cook Aromatics: Add oil to large oven-safe pot over medium heat. Once heated, add onions and cook until turning light brown, about 5 minutes, stirring occasionally. Stir in all dried seasonings for a minute to release aromatics. Stir in tomato paste for a minute until well-mixed. Browned bits should be forming along bottom of pot, adding flavor to dish. Turn off heat.
Add Acid & Pork: Add apple cider vinegar and balsamic vinegar. Stir everything together, using stiff wooden utensil to loosen browned bits stuck to bottom of pot. Add pork chunks, stirring with other ingredients until well-coated with sauce.
Bake: Transfer pot to oven. Bake uncovered for 1 hour, remove and stir, then bake uncovered for another hour or until pork is very tender. As pork cooks, liquid will be released and any meat sitting above liquid level will be nicely browned.
Thicken Sauce: Transfer pot to stovetop. Turn on medium heat and boil for about 10 minutes to thicken from watery liquid to sauce-like consistency. While boiling, use stiff wooden utensil to occasionally scrape along bottom of pot to prevent sticking. Turn off heat.
Serve: Serve pork with sauce , rice and beans .