Heat the oil in a 4-quart pot over low-medium heat. Add the onion, garlic, peppers, salt, and pepper to taste. Cover and cook, stirring occasionally, for about 15 minutes, until the vegetables are just tender and have released some of their liquids. Add the baked beans, barbecue sauce, mustard, and crumbled veggie burgers. Stir well to combine. Cover and continue cooking for about 3 minutes, stirring occasionally until heated through. Taste for seasonings.