Combine white sugar and warm water in a large bowl or in a work bowl of a stand mixer. Sprinkle yeast over warm sugar water, and let stand for 5 minutes until yeast softens and forms a creamy foam. Stir 1 tablespoon olive oil into yeast mixture.

Stir 1/2 teaspoon salt into flour. Mix half of flour mixture into yeast water, and stir until no dry spots remain. Stir in remaining flour, a 1/2 cup at a time, mixing well after each addition. Knead until smooth and elastic, about 8 minutes.

Lightly oil a large bowl, place dough in the bowl and turn to coat with oil. Cover with a light cloth, and let rise in a warm place until doubled in volume, about 1 hour.

Combine crushed tomatoes, brown sugar, garlic powder, olive oil, and salt in a saucepan. Cover and cook over low heat until the tomatoes start to break down, about 30 minutes.

Deflate dough and turn it out onto a floured surface. Roll one piece into a 12-inch thin circle and the other into a thicker, 9-inch circle.

Assemble the pizza: Place the 12-inch dough round into a springform pan. Layer cheese, sausage, pepperoni, mushrooms, peppers, and remaining cheese. Top with the 9-inch dough round, seal edges, and add sauce.

Bake pizza in the oven at 450°F (230°C) until crust is set, cheese melts, and sausage is cooked through, approximately 40–45 minutes.