Mix the flour, water, olive oil, salt, and yeast together. Knead the dough until smooth and uniform, then divide it into two equal parts.

Let the dough rise until it doubles in size.

Preheat the oven to 480°F (250°C). Meanwhile, roll out the dough on a round baking sheet. Top with tomato puree, mozzarella, cooked ham, and mushrooms. Fold the dough over to form a half-moon shape, then spread a tablespoon of tomato puree on top of the calzone. Bake for the first 10 minutes at 480°F (250°C), then reduce the temperature to 400°F (200°C) and bake for another 20 minutes.