Combine flour mix and yeast packet in a large mixing bowl with 1 1/4 cups lukewarm water. Stir with a fork until dough begins to form.
Knead by hand for 3 minutes, or until dough is soft and smooth. Transfer to a clean, lightly oiled bowl and cover tightly with plastic wrap. Allow the dough to rise in a warm place until doubled, about 45 minutes. (After this step, you can refrigerate for use within 1-3 days.).
Preheat the oven to 500F.
Heat 2 tablespoons of the butter in a large saucepan over medium heat until melted and sizzling. Add ½ of the sliced onions to the pan. Cook and continue to stir until onions are soft and beginning to turn translucent, about 1-2 minutes. Stir in a few more handfuls of the onion and repeat cooking and stirring process until all onions are cooked. Season with a pinch of salt.
Reduce heat to medium-low and continue to simmer onions, stirring every few minutes to prevent them from sticking and coloring too much in any one place. Cook until golden brown, about 30-35 minutes.
Drizzle 2 tablespoons of the olive oil in a 17" X 11.5" jelly roll pan or baking sheet. Gently press and poke the dough into the pan with your fingers, working it into the corners. If the dough springs back, let it rest for about 10 minutes for the gluten to relax. Cover with plastic wrap and set in a warm area of the kitchen to rise for another 30 minutes or until it has doubled in size.
Evenly spread the sauce over the dough, leaving a 1/2 -inch border around the edges. Scatter the cooked onions and peppers over the sauce. In any even layer, arrange the meatballs on top, then sprinkle with the cheese.
Bake until the cheese is bubbling and beginning to brown, 12-14 minutes. Remove from oven and let stand for 2 minutes. Slice and serve.