Make the dough: Put a pizza stone or inverted baking sheet on the lowest oven rack and preheat to 450 degrees F. Combine the flour, baking powder and salt in a large bowl. Add the water and olive oil and mix to make a shaggy, sticky dough. Turn out onto a lightly floured surface and knead into a smooth and elastic ball, 2 to 3 minutes. Divide the dough in half and shape each half into a flat disk. Wrap each disk in plastic wrap and let rest in a warm place, 15 minutes.
Brush two large sheets of parchment paper with olive oil. Place a ball of dough between the parchment, oiled-sides in; use a rolling pin to roll the dough into a 12- to 14-inch round, about 1/8 inch thick. Remove the top piece of parchment and transfer the dough (and the bottom piece of parchment) to a pizza peel or inverted baking sheet.
Spread 1/3 cup sauce on the crust; scatter with 3/4 cup mozzarella. Slide the pizza (on the parchment) onto the hot stone. Bake until the crust is crisp and golden brown and the cheese is bubbling, 10 to 12 minutes. Transfer to a cutting board and let cool 1 to 2 minutes before slicing. Repeat to make the second pizza.
You don't have to let this dough rise: There's no yeast in it. The dough can be sticky, so roll it out between oiled parchment paper to get it super thin.