Make the dough: In a large bowl, combine warm water, yeast, and sugar. Let sit for 5-10 minutes until foamy. Stir in olive oil, salt, and 3 cups of flour. Mix until a shaggy dough forms.
Knead: Turn dough onto a floured surface. Knead for about 8-10 minutes, adding remaining flour as needed until the dough is smooth and elastic but still slightly tacky. Do not over-flour.
Rise: Place dough in an oiled bowl, turning once to coat. Cover with a damp towel or plastic wrap. Let rise in a warm place for 1-2 hours, or until doubled in size.
Prepare filling: While dough rises, whisk together ricotta, ½ cup mozzarella, Parmesan, eggs, parsley, and pepper in a small bowl. Set aside.
Divide and shape: Punch down risen dough. Divide into 4 equal portions. Roll each portion into an oval about 1/8-inch thick on a lightly floured surface.
Fill: Spoon filling onto one half of the oval, leaving a 1-inch border. Fold the other half over the filling to create a half-moon shape.
Seal: Press edges firmly with your fingers. Then, use a fork to crimp the edges tightly all around. Poke 2-3 small slits in the top of each calzone with the fork tip to allow steam to escape.
Bake: Place calzones on a parchment-lined baking sheet. Brush tops lightly with olive oil or egg wash for browning (optional). Bake at 400°F (200°C) for 15-18 minutes until golden brown and crispy.
Cool slightly: Let cool for 5 minutes before slicing to allow cheese to set. Serve warm with marinara sauce on the side.