Cut your pork roast into large chunks and trim off any excess fat.
Place pork into a Dutch oven set over medium high heat on the stovetop along with the olive oil and sear on all sides. Then remove the meat and set it aside.
Reduce the heat to medium and add the chopped onions and green peppers to the rendered fat left in the pot. Saute the vegetables until tender while stirring frequently, then add the minced garlic and cook for another two minutes.
Stir the flour into the vegetable mixture along with all of the chili seasonings. Stir to disperse it evenly and let it cook for about a minute to help the flavors bloom.
Return the pork to the pot and stir in the undrained tomatoes, along with the tomato sauce, tomato paste, chili beans, barbeque sauce, Worcestershire sauce, and beef stock. Mix well to combine.
Reduce the heat to low and let the chili simmer for 3 hours uncovered or until the pork is easily shredded with a fork. Stir occasionally while simmering to prevent scorching on the bottom of the pot.
Serve in bowls with your favorite toppings.