Preheat the oven to 325°F (163°C).

Cut 2 pounds pork shoulder into 1-inch cubes and pat dry with paper towels.

Heat 2 tablespoons olive oil in a Dutch oven over medium-high heat until shimmering.

Working in batches, brown the pork cubes on all sides for 3 to 4 minutes per batch; transfer to a plate.

Add 1 large diced onion and cook for 4 minutes until softened.

Stir in 4 cloves minced garlic and cook for 1 minute, scraping up any browned bits.

Add 1 can (6 ounces) tomato paste and cook for 2 minutes, stirring constantly to caramelize.

Pour in 1 cup chicken broth and deglaze the pot, scraping up any browned bits.

Stir in 3 tablespoons brown sugar, 2 tablespoons apple cider vinegar, 1 tablespoon Worcestershire sauce, 1 teaspoon dry mustard powder, 1 teaspoon smoked paprika, salt, pepper, 2 bay leaves, and the browned pork.

Cover the pot and braise in the oven for 60 minutes.

Remove the pot, stir in the drained beans, and return to the oven uncovered for 30 minutes.

Remove from the oven, discard the bay leaves, taste, and adjust seasoning with salt, pepper, or vinegar as desired.