Place a large saute pan with 2 tablespoons oil over medium heat. Add the onions, peppers, garlic, and salt and pepper, to taste. Saute until vegetables are softened, about 2 to 3 minutes.
Preheat grill to medium-high.
On a floured surface, roll each piece of dough into a 6-inch circle. Brush both sides of dough with oil and place directly onto grill. Close grill top for 1 to 2 minutes, then flip and cook the other side. Remove from the grill.
Brush BBQ sauce evenly over each pizza. Place sauteed vegetables and pork on top. Sprinkle with mozzarella and Parmesan cheese and place back onto the grill. Close the lid for 2 to 3 minutes or until the cheese melts.
In a medium saucepan, combine all ingredients. Bring mixture to a boil, reduce heat to simmer. Cook uncovered, stirring frequently, for 1 hour 15 minutes.