Mix together pork, fennel, Parmigiano, 3/4 teaspoon salt, and 1/2 teaspoon pepper in a bowl. Form into 1 1/2-inch balls. Heat oil in a large straight-sided skillet over medium-high. Add meatballs and cook, turning occasionally, until golden brown, 5 to 6 minutes; transfer to a plate.

Add peppers, onion, and 1/4 cup water to skillet and cook, stirring occasionally, 4 to 6 minutes. Stir in tomato sauce and 3/4 cup water. Season with salt and pepper and return meatballs and any accumulated juices to pan. Bring to a boil, then reduce heat to low. Partially cover skillet and simmer until meatballs are cooked through, about 10 minutes.

Preheat broiler, with rack 6 inches below element. On a baking sheet, drizzle both sides of bread with oil. Broil, flipping once, until toasted. Nestle into skillet and top everything with mozzarella. Broil until cheese melts, about 2 minutes. Sprinkle with basil and serve.