In the bowl of an electric mixer fitted with the dough hook, combine the flour, baking powder, and salt.
Mix 1/2 cup plus 2 tablespoons water and the olive oil in a cup and, with the mixer on medium speed, pour the wet ingredients into the dry.
Knead the dough in the mixer until soft and smooth, about 2 minutes.
Remove the dough, and knead on a well-floured counter a few times, then wrap in plastic and let rest at room temperature while you make the topping.
Preheat oven to 450° with a pizza stone on the bottom rack.
Drain and crush the canned tomatoes, squeezing out as much juice as possible; coarsely chop the tomatoes and put in a medium bowl; add in the crushed garlic, olive oil, and salt; let steep 10-15 minutes.
After the garlic has steeped, discard it and stir in the basil.
Combine the three cheese in a food processor, pulsing until cheese is mixed to a crumbly paste.
Divide the dough in half; on a floured work surface, roll the dough into an 11-12 inch round.
Put the dough on a floured pizza peel, or on the back of a baking sheet lined with parchment paper.
Spread with half of the sauce, all the way to the edges of the dough.
Top with half of the cheese.
Slide the pizza off the pizza peel or baking sheet with parchment onto the pizza stone.