In a large mixing bowl, combine the active sourdough starter, warm water, and olive oil. Stir to combine.
Add the all-purpose flour and salt to the bowl. Mix until a shaggy dough forms.
Turn the dough out 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 damp cloth or plastic wrap, and let it rise at room temperature for 4-6 hours or until doubled in size.
Preheat your oven to 425°F (220°C). Lightly grease a 10-inch deep dish pizza pan or cast iron skillet with olive oil.
Gently deflate the risen dough and press it evenly into the bottom and up the sides of the prepared pan.
Spread the crushed tomatoes evenly over the dough base. Sprinkle the dried oregano, dried basil, garlic powder, salt, and pepper over the tomato sauce.
Layer the shredded mozzarella cheese evenly over the sauce.
Distribute the cooked ground beef, sliced mushrooms, green bell pepper, and onions evenly over the cheese layer.
Bake the pizza in the preheated oven for 35-45 minutes, or until the crust is golden brown and cooked through, and the cheese is bubbly and slightly browned.
Remove the pizza from the oven and let it cool for 5-10 minutes before slicing and serving.