Ultra-Thin-Crust Pizza with Onions, Mushrooms, and Ricotta Recipe

Olive oil
1 small red onion, halved and thinly sliced
Pinch of sugar
1 teaspoon balsamic vinegar
2 large flour tortillas (sandwich wraps)
1 cup shredded Asiago cheese (about 2 ounces)
2/3 cup ricotta cheese
6 button or cremini mushrooms, trimmed and thinly sliced
Kosher salt and freshly ground black pepper
Equipment needed:
It really helps to have a baking stone and a pizza peel. If not, you’ll use a rimmed baking sheet with some parchment paper.
1a If you are using a baking stone, place the stone on top of the middle rack in the oven. Preheat the oven to 450°F. Allow the oven to stay at 450°F for at least 15 minutes before cooking, to thoroughly heat up the stone.
1b If you are NOT using a baking stone, place racks in the upper and lower thirds of the oven. Preheat the oven to 450°F.

2 Heat 1 Tbsp olive oil in a small sauté pan on medium hight heat. Add the sliced onions and cook, stirring occasionally, until the onions begin to soften. Add a pinch of sugar and the balsamic vinegar, cook for a few more minutes until the onions are thoroughly softened and translucent. Remove from heat.
3a If you are using a baking stone, sprinkle some corn meal on your pizza peel and place one tortilla on top of the pizza peel. (If you don’t have a pizza peel, you can use a rimless baking sheet.) Thoroughly brush the top of the tortilla with olive oil.
3b If you are not using a baking stone, line two rimmed baking sheets with parchment paper and brush with olive oil. Place a tortilla on each baking sheet and brush each with olive oil.

4 Sprinkle each tortilla with half a cup of shredded Asiago cheese. Add bits of ricotta cheese, 1/3 cup for each tortilla. Sprinkle with mushrooms and with the slightly caramelized onions. Sprinkle with a little salt and pepper.
5a If you are using a baking stone, and can fit both pizzas on the stone (it depends on the size of your tortilla) do it. Use the pizza peel to transfer the pizzas to the stone in the oven. If your tortillas are large, you’ll need to cook them one at a time. But that’s okay. Cooking on the stone goes very quickly. Bake the pizzas until the crust is crisp and very brown - 5-7 minutes using the baking stone. Cut with a pizza cutter or a knife.
5b If you are using baking sheets, place the baking sheets in the oven. Bake until the crust is crisp and brown all over (the time varies, depending on the oven and if your cookie sheet has already been heated, start with 10 minutes and check), rotating the sheets to ensure even baking. Cut with a pizza cutter or a knife.
Each pizza serves 1-2, depending on how hungry you are.

Really sounds good! Have you tried using the flat-out breads for this at all?

I notice you use a baking stone.  I've been looking into them but there are so many different types I'm not certain which is the best.  Any ideas?  I've noticed that some now have handles to make it easier to lift out of the oven.