All ingredients ready? Let's begin!
In a large mixing bowl, combine the warm water and yeast. Sprinkle the sugar on top of the water and yeast. Set this aside for about 5 minutes until the yeast starts to bloom or bubble.
Gently stir the salt and 1 teaspoon of olive oil into the blossomed yeast.
Add the flour and stir to combine well until the dough comes together into a ball.
Lightly flour a flat work surface. Turn the dough onto the floured surface and knead with the heels of your hands for 5 minutes, dusting with a little more flour if too sticky. (Alternatively, you can make the dough in a stand mixer with a dough hook attachment).
Wipe out the bowl. Add the remaining teaspoon of oil to the bowl and rub it onto the sides of the bowl. Place the ball of dough in the bowl and rotate it so the oil coats it.
Cover the bowl with a clean kitchen towel or plastic wrap and place the bowl in either a cold oven or a microwave away from drafts or moisture.
Allow the dough to proof until it doubles in size, approximately 60 minutes.
Make 24 smaller balls of dough and place them on a lightly floured work surface.
Roll each ball out into a 3-inch circle at approximately ¼-inch thick.
Place the pizzas on a floured or parchment-lined sheet pan or two, cover with a clean dishtowel, and allow them to rest for approximately 30 minutes to rise again.
Meanwhile, slice your tomatoes, slice the basil, and combine the 2 cheeses.
In a large skillet over medium-high heat, warm about ½ inch of oil. When the oil is hot, start frying the pizza dough in a single layer for 2 minutes per side until golden brown. Drain on butcher’s paper or paper towels quickly and place them on a serving platter. Top immediately with a tomato slice, basil, salt, pepper, and cheese.
Continue frying and topping the dough until all are cooked. Serve while still warm and crisp.