Preheat oven to 400 degrees F. Heat 1 tablespoon olive oil and onion in a small skillet over a medium heat. Cook until onion is translucent. Stir in the garlic and set aside to cool.
Sprinkle a pizza paddle with a little cornmeal. Place the rolled out pizza dough onto the paddle or place pizza dough onto a cooling rack that is at least as large as the rolled out dough. Using the paddle, slide the dough directly onto the oven rack in the center of preheated oven, or place the cooling rack in the center of preheated oven. Cook until dough is slightly firm, about 3 minutes. This will allow you to easily slide the pizza off of the paddle or cooling rack once the toppings are on it.
When the dough is slightly firm, carefully remove from oven using the paddle or by removing the cooling rack. Do not turn oven off. Brush dough with remaining olive oil and evenly spread out the garlic/onion mixture over the dough, leaving a ½ inch border. Sprinkle with the two cheeses.
Place pizza back into oven. Continue to cook until the crust is crisp and the cheese melts, about 7-10 more minutes. Check occasionally. While pizza is cooking, in a medium bowl, toss together greens, tomatoes, cucumber, and basil. Dress with olive oil and vinegar. Salt and pepper to taste.
Remove pizza from oven and top with salad. Cut with pizza cutter or large knife.