Preheat the oven to 375 degrees . In a greased 9-inch pie plate, overlap the tortillas to make a crust; place on a rimmed baking sheet. Meanwhile, fill a large nonstick skillet a third of the way with salted water; bring to a boil. Add the asparagus and cook until crisp-tender, about 1 minute; drain, rinse under cold water and pat dry.
Wipe out the skillet, add the olive oil and heat over medium-high heat. Add the onion and mushrooms, season with salt and pepper and cook until the mushrooms are golden, about 3 minutes. Stir in the asparagus; season with salt and pepper. Spread evenly in the tortilla crust, then crumble the cheese on top.
In a medium bowl, whisk together the eggs and yogurt and season with salt and pepper; pour into the tortilla crust. Bake on the baking sheet until just set in the center and lightly golden, about 30 minutes. Let rest for about 10 minutes before serving.
