Special equipment: a 4 1/2-inch biscuit cutter, optional
For the marinara sauce: In an 8-inch saucepan, add the olive oil along with the onion and turn the heat to medium. Add a small pinch of salt and saute until the onion softens and develops a bit of color, about 6 minutes. Add the garlic and cook for 1 minute more. Add the tomatoes along with the sugar and oregano, partially cover the saucepan with a lid, bring to a simmer and cook until the sauce reduces and deepens in color, about 20 minutes.
Remove the lid, add the basil, season with salt and pepper to taste and cook for 5 additional minutes.
For the pizza: Preheat the oven to 400 degrees F. Sprinkle some semolina on a couple of baking sheets and set aside.
Roll out each ball of dough into a 15-inch circle using either your hands or a rolling pin. Using a large biscuit cutter or an upside-down bowl, cut out 4 1/2-inch circles and place them on the prepared baking sheets. Top the mini pizzas with some of the marinara sauce, followed by your desired toppings, making sure to leave a little border all around. Bake until golden brown and bubbly, 8 to 10 minutes.
Add the warm water in a small bowl and sprinkle over 1 teaspoon of the sugar and the yeast; set aside so the yeast can proof.
Oil two bowls with a little olive oil and set aside.
In the bowl of a stand mixer fitted with a dough attachment, mix together the olive oil, salt, 3 1/2 cups of the flour and the remaining 1 1/2 teaspoons sugar. Stir the yeast in the water to make sure its all dissolved and add it to the flour mixture. Mix on medium-low speed until everything is combined. Increase the speed to medium and allow the machine to knead the dough, adding more flour if necessary, until it is smooth and comes away from the side of the bowl, 6 to 7 minutes.
Divide the dough in two pieces and roll each into a ball. Place a ball in each of the oiled bowls seam-side down, and brush the tops with a little oil to stop them from drying out. Cover the bowls with plastic wrap and place in a warm place (inside a microwave or a turned-off oven works best) until it doubles in size and when poked with a finger, the indent remains (it doesn't spring back), about 1 1/2 hours.
Once the dough has risen, use immediately or store in the refrigerator for up to 24 hours.