Preheat the oven to 425°F (220°C).
In a bowl, combine warm water, yeast, and sugar. Let it sit for 5 minutes until frothy.
Add flour, olive oil, and salt to the yeast mixture and knead until smooth.
Let the dough rise in a warm place for 30 minutes.
Roll out the dough and place it in a deep-dish pizza pan.
Spread pizza sauce evenly over the dough.
Layer mozzarella cheese, pepperoni, bell peppers, and mushrooms on top.
Bake for 25-30 minutes or until the crust is golden brown.
Let it cool for a few minutes before slicing and serving.