Tortilla Pizza with Onions, Mushrooms, and Ricotta

olive oil, plus more for brushing on tortilla and pan

small red onion, halved and thinly sliced, about 3/4 cup sliced onion

sugar

balsamic vinegar

large flour tortillas (sandwich wraps)

shredded Asiago cheese

ricotta cheese

 button or cremini mushrooms, trimmed and thinly sliced

Kosher salt and freshly ground black pepper