To prepare the dough, in a small bowl, combine the yeast, water and sugar and whisk by hand until dissolved. Let stand for 5 minutes. In the bowl of a food processor, combine the vegetable oil, flour and salt. Place the bowl on the processor''s motor, attach the dough hook. Turn the food processor on to dough-speed, and slowly add the yeast/water liquid. Knead on low speed until smooth and pliable, about 5 minutes.
Transfer dough to a plate or bowl. Cover loosely with plastic wrap and let the dough rise at room temperature for 2 hours.
Position a rack in the lower third of an oven and preheat to 450°F.
Put olive oil in 4 mini deep-dish pizza pans (about 2 tsp. per pan), thoroughly greasing each pan. Divide dough into 4 equal balls. Place a dough ball in each pan and, using your fingers, press the dough in an even layer across the bottom and up the sides of the pans.
Add sauce, cheese, and desired toppings.
Bake the pizzas until the crusts are golden, 30 to 35 minutes. Remove the pizzas from the oven and let stand for 5 minutes before serving.
Makes 4 mini deep-dish pizzas.
