In a large mixing bowl, combine the sourdough starter, warm water, and olive oil. Stir to combine.
Add the all-purpose flour and salt to the bowl. Mix until a rough dough forms.
Turn the dough onto a lightly floured surface and knead for about 8-10 minutes until smooth and elastic.
Place the dough in a lightly oiled bowl, cover with a clean kitchen towel or plastic wrap, and let it rise at room temperature for 4 to 6 hours or until doubled in size.
While the dough is rising, prepare the tomato sauce. In a medium saucepan over medium heat, add a tablespoon of olive oil and sauté the minced garlic until fragrant, about 1 minute.
Add the crushed tomatoes, dried oregano, dried basil, sugar, salt, and black pepper to the saucepan. Stir to combine and simmer for 20 minutes, stirring occasionally. Remove from heat and set aside.
Preheat your oven to 425°F (220°C).
Once the dough has risen, lightly oil a 10-inch deep dish pizza pan or cast iron skillet.
Gently press the dough into the pan, pushing it up the sides to form a thick crust.
Sprinkle half of the shredded mozzarella cheese evenly over the dough.
Distribute the cooked ground beef, sliced green bell pepper, and sliced onion evenly over the cheese layer.
Pour the tomato sauce over the toppings, spreading it evenly.
Sprinkle the remaining mozzarella cheese over the sauce, then top with grated Parmesan cheese.
Bake the pizza in the preheated oven for 40 to 45 minutes, or until the crust is golden brown and the cheese is bubbly and slightly browned.
Remove the pizza from the oven and let it cool for 10 minutes before slicing and serving.