Warm the olive oil in large skillet over medium-high heat, and add the Beyond Beef to the skillet. Break the beef up into small pieces and cook for 10 minutes without moving the pieces around. This will brown the 'beef'. Turn the pieces over using tongs, and continue to cook for another 5 minutes.
Remove the 'beef' from the skillet and set aside. Add the bell pepper and onion to the skillet. If the skillet is completely dry, add a little olive oil. Sauté until slightly softened, about 5 - 7 minutes. Add the garlic, and sauté for another 2 minutes.
Stir in the tomato paste until it's completely mixed into the veggies.
Add the ketchup, 1/2 cup water, brown sugar, mustard, chili powder, oregano, Worcestershire sauce, salt and pepper. Stir until well-combined and add the 'beef' back in.
Cook on a low simmer for 20 minutes. Add additional water if the Sloppy Joe sauce is too thick. Finish with a dash of hot sauce, if desired.
Spoon over warmed rolls and top with Vegan Coleslaw.