Make the Dough: In the bowl of a standing mixer, whisk together flour, yeast, and salt to combine. Attach the dough hook, and with the mixer running at medium-low speed, add olive oil, then gradually add water. Continue to mix until the mixture comes together and a smooth, elastic dough forms, about 10 minutes.
Coat a large bowl with non-stick cooking spray. Transfer the ball of dough to the bowl, turn to coat, and cover with plastic wrap. Let rise in a warm, draft-free area until doubled in size, about 1½ to 2 hours.
Prepare the Filling: While the dough rises, combine ricotta cheese, half of the mozzarella, and half of the provolone in a bowl. Cover with plastic wrap and refrigerate until needed. If using any additional fillings like vegetables, sauté them and place on a paper towel-lined plate to drain.
Assemble the Calzones: Adjust an oven rack to the lowest position, place a pizza stone on the oven rack, and preheat the oven to 500 degrees. Line a baking sheet with parchment paper and spray the parchment with non-stick cooking spray.
Turn the risen dough out onto an unfloured work surface. Divide the dough into six equal pieces and gently shape each piece of dough into a ball. Transfer the balls of dough to the baking sheet and cover with lightly sprayed plastic wrap. Let the dough rest for at least 15 minutes, but no more than 30 minutes.
Working with one piece of dough at a time, roll it into a 9-inch circle. Spread one-sixth of the ricotta mixture on the bottom half of the dough round, leaving a 1-inch border. Top with your desired fillings and one-sixth of the remaining mozzarella and provolone cheeses.
Fold the top half of the dough over the filled bottom half, leaving a ½-inch layer of the bottom layer uncovered. With your fingertips, press around the cheese filling and out to the edge to lightly seal the dough. Starting at one end of the calzone, place an index finger diagonally across the edge and gently pull the bottom layer of dough over the tip of your index finger; press into the dough to seal. Repeat until the calzone is fully sealed.
With a paring knife, cut five slits, about 1½ inches long, diagonally across the top of the calzone. Repeat with the remaining balls of dough until all of the calzones are assembled.
Brush the tops and sides of each of the calzones with olive oil. Dust a pizza peel with flour and transfer three of the calzones to the baking stone. Bake until golden brown, about 11 to 15 minutes. Remove to a wire cooling rack and allow to cool for at least 5 minutes before serving. Once you remove the first batch, bake the second batch of calzones.
Make the Tomato Dipping Sauce: When you put the first batch of calzones in the oven, start the dipping sauce. Place garlic and olive oil in a medium saucepan over medium heat. When the garlic starts to sizzle, add the crushed tomatoes. Simmer uncovered until the sauce thickens, about 15 minutes. Season to taste with salt and pepper.