Heat the oven to 500 degrees. Lightly oil a baking sheet and on it spread out the tortillas in a single layer. Distribute a portion of the mushrooms over each one, then the cheeses and olives. Drizzle 2 tablespoons of salsa over each "quesadilla," then set the baking sheet in the oven. In 5 to 6 minutes, the tortillas should be crispy underneath and the cheese melted. Remove from the oven. While the quesadillas are baking, in a medium-size bowl, toss the frisee (or other greens) with the lime or vinegar, salt and cilantro. Transfer each quesadilla to a warm plate, then top with a portion of lettuce right in the center. Serve without delay.
Recipe courtesy of Rick Bayless, "Salsas That Cook"