In a small saucepan, combine the tomato sauce, tomato paste, Italian seasoning, and sugar. Whisk until well combined. Bring to a gentle boil, then reduce the heat and simmer for 5 minutes. Remove from heat.
Preheat your oven to 375ºF and line a baking sheet with parchment paper.
Place each half of the Italian bread crust side down on the baking sheet. Spread ½ cup of pizza sauce evenly over each half. Sprinkle ½ cup of cheese over the sauce on each half, followed by half of the pepperoni and diced green pepper.
Bake for 15 minutes. Check for golden brown edges and melted cheese. If needed, bake for an additional 5 minutes.
Let the pizza cool for 5 minutes before slicing and serving.