Make the dough: In the bowl of a stand mixer, whisk together 4 cups (500 g) bread flour, 2¼ teaspoons (2.25 teaspoons) instant yeast, and 1½ teaspoons (1.5 teaspoons) salt. Fit the mixer with the dough hook and run at medium–low speed. Add 2 tablespoons olive oil, then gradually add 1½ cups (375 ml) plus 1 tablespoon warm water (about 105°F) while the mixer runs. Continue mixing until the dough comes together into a smooth, elastic ball, about 10 minutes.

First rise: Lightly coat a large bowl with a thin layer of olive oil, transfer the dough ball to the bowl, turn to coat all sides in oil, and cover the bowl with plastic wrap. Let the dough rise in a warm, draft-free place until doubled in size, about 1½ to 2 hours.

Prepare the filling and toppings: While the dough rises, combine the 15-ounce (425.24 g) container ricotta with half of the shredded mozzarella (8 oz) and half of the shredded provolone (8 oz). Cover and refrigerate this ricotta mixture until needed. If you are using cooked toppings (sausage, vegetables, etc.), cook them now and drain on paper towels.

Preheat the oven and prepare baking surface: When the dough is nearly ready to be shaped (toward the end of the rise), place a pizza stone on the lowest oven rack and preheat the oven to 500°F. Line a baking sheet with parchment paper and lightly coat the parchment or sheet with olive oil so the dough balls do not stick.

Divide and rest the dough: Turn the risen dough out onto a work surface. If the dough is sticky, lightly dust the surface with a little of the bread flour. Divide the dough into six equal pieces and gently shape each piece into a smooth ball. Transfer the six dough balls to the prepared baking sheet, cover loosely with plastic wrap, and let rest for at least 15 minutes and no more than 30 minutes.

Assemble one calzone at a time: Working with a single dough ball, lightly dust it with a bit of bread flour if needed and roll it into a 9-inch (about 23 cm) circle. On the bottom half of the circle, spread one-sixth of the ricotta mixture, leaving a 1-inch border around the edge. Add your desired toppings, then sprinkle one-sixth of the remaining shredded mozzarella and one-sixth of the remaining shredded provolone over the toppings.

Fold and seal: Fold the top half of the dough over the filled bottom half to enclose the filling. Press the dough together around the filling to expel any large air pockets, then pinch and crimp the edge firmly to seal so no filling can escape. Using a paring knife, cut five slits about 1½ inches long across the top of the calzone to vent steam. Place the finished calzone on the parchment-lined baking sheet. Repeat steps 6–7 for the remaining dough balls.

Brush and transfer to the oven: Brush the tops and sides of each calzone with olive oil (the olive oil listed for brushing). Lightly dust a pizza peel with a little bread flour so the calzones slide easily, then transfer three calzones at a time to the preheated pizza stone.

Bake and cool: Bake the calzones until golden brown, about 11 to 15 minutes. Remove the baked calzones to a wire rack and let cool at least 5 minutes before serving. After removing the first batch, bake the remaining calzones in the same way.

Make the tomato dipping sauce (start when the first batch goes into the oven): In a medium saucepan over medium heat, warm 2 tablespoons olive oil and add the 2 minced garlic cloves. As soon as the garlic starts to sizzle and becomes fragrant (watch carefully so it does not brown), add the 28-ounce (793.79 g) can crushed tomatoes. Simmer uncovered until the sauce thickens, about 15 minutes. Season to taste with salt and pepper.