Mix 1 cup flour, sugar, and yeast in bowl. Stir in the water and oil until blended. Pulse 1 3/4 cups flour and salt in food processor to mix. Add yeast mixture and pulse until blended. With motor running, add remaining flour, 1 tablespoon at a time, until soft dough forms (you will need to process about 2 minutes). Dough is ready when it comes together in a ball.
Dust work surface lightly with flour. Turn out dough and knead until smooth, 1 to 2 minutes. Roll dough into 1 1/2-inch balls in your hands. Then flatten into 3-inch rounds. Cover with clean kitchen towel; let rest 10 minutes.
Preheat oven to 450°F Line two baking sheets with parchment paper. Divide dough into 4 pieces. Wrap 3 in plastic; refrigerate. Cut remaining dough into 12 equal pieces; shape each into 1 1/2-inch ball. Arrange on baking sheets; flatten into 3-inch rounds. Lightly coat with nonstick cooking spray.
Cut tomatoes into thin slices, then fan out slices. Top each pizza with 2 or 3 slices. Sprinkle with 1 teaspoon fontina, a little Parmesan, plus a few olive slivers and oregano leaves. Bake until bubbly and crust is golden, about 10 minutes. Repeat with remaining dough.
To keep dough from sticking to the food processor, lightly coat the inside of the bowl with nonstick cooking spray.