Preheat your oven to 425°F (220°C).
In a bowl, combine warm water, sugar, and yeast. Let it sit for 5 minutes.
In a large mixing bowl, combine flour and salt.
Add the yeast mixture and olive oil to the flour.
Knead the dough until smooth, about 5 minutes.
Let the dough rise in a warm place for 30 minutes, covered.
Roll out the dough to fit a deep dish pizza pan.
Place the dough in the pan, pushing it up the sides.
Spread mozzarella cheese evenly across the bottom.
Layer cooked sausage, black olives, and crushed tomatoes over the cheese.
Bake in the preheated oven for 30-35 minutes until golden brown.
Let it cool for 10 minutes, garnish with basil, and serve.