Preheat your oven to 325°F (165°C).
Season the 2 to 3 pounds pork shoulder chunks with 1 teaspoon salt and 1 teaspoon black pepper.
In a large Dutch oven, cook the 4 slices chopped bacon over medium heat until crispy. Remove the bacon and set aside, leaving the fat in the pot. If skipping bacon, add 1 tablespoon oil.
Increase the heat to medium high and add the pork shoulder pieces. Sear for 3 to 4 minutes per side until browned. Work in batches if needed. Remove the pork and set aside.
In the same pot, add the diced onion and cook for 4 to 5 minutes until softened. Stir in the 4 cloves minced garlic and cook for 30 seconds.
Pour in 1 ½ cups chicken broth, scraping up any browned bits from the bottom of the pot.
Stir in 1 cup tomato sauce, ⅔ cup ketchup, ⅓ cup molasses, 3 tablespoons brown sugar, 2 tablespoons apple cider vinegar, 1 tablespoon Worcestershire sauce, 2 teaspoons dry mustard powder, and 1 teaspoon smoked paprika.
Add the 3 cans drained and rinsed navy beans and stir to combine.
Return the seared pork and cooked bacon to the pot, nestling the pork into the beans. Cover and transfer to the oven. Cook for 2 to 2 ½ hours, until the pork is tender and easily pulls apart.
Remove from the oven and break up the pork into large chunks using a spoon or fork. If you want a thicker sauce, return the pot to the oven uncovered for 15 to 20 minutes.
Let sit for 10 minutes before serving.