*To make the mozzarella easier to slice, put in freezer for about 5 minutes.
Mix yeast and sugar into water; let stand 5 minutes; stir in 2 tablespoons olive oil.
In a food processor or bowl, mix flour and salt.
With machine running or with fingertips if making by hand, combine yeast mixture with flour and salt mixture until a soft dough forms. If dough is too dry, add more water a little at a time; if too sticky, add more flour a little at a time.
On a lightly floured work surface, knead dough about 2 minutes; divide into two balls. Cover dough with a tea towel. Let rest for 10 minutes; punch down into two flat disks.
Beginning in the center, press balls of dough into 8-inch rounds with raised edges. Brush a large baking sheet with olive oil and place the two rounds of dough on the baking sheet.
Brush each round with 1 tablespoon olive oil; evenly sprinkle half of the garlic and half of the Parmesan cheese over each round.
Evenly scatter half of the tomatoes and half of the mozzarella over each pie. Lightly drizzle additional olive oil over the cheese.
Bake at 450° until crust and cheese are lightly browned, about 10 minutes.
Scatter with basil; let rest 5 minutes, then cut into eight wedges.