1large leektrimmed and sliced, white and light green parts only
8ouncessliced mushroomsany kind, or a mix
Kosher or coarse salt and freshly ground pepper to taste
6 6-inchcorn or corn and flour tortillas
2cupsshredded Monterey Jackor a combo of Monterey jack and mozzarella
Avocadosliced red onion and salsa for serving
Preheat the oven to 400°F.
Heat 1 tablespoon of the oil in a skillet over medium heat. Add the leeks, season with salt and pepper and sauté for about 5 minutes until they start to soften. Add the mushrooms and continue to saute for another 8 minutes or so. The mushrooms will soften and probably release some liquid as they cook. Continue cooking until all of the liquid has been released, and evaporated, and the mushrooms and leeks start to brown a bit. Turn the vegetables onto a plate and set aside.
Wipe out the skillet, then return it to medium heat and add the rest of the oil. Place a tortilla in the pan and cook for 1 minute, then flip the tortilla. Cook for another 60 seconds until the tortilla is fairly firm and crisp. Transfer the tortillas to a rimmed baking sheet in a single layer as you finish, then continue with the tortillas one at a time.
Divide half of the the cheese evenly over the tortillas, and distribute the sautéed vegetable mixture evenly over the tops. Sprinkle over the rest of the cheese evenly. Bake until the cheese is melted, about 3 minutes.
Meanwhile, pour off all but a couple of teaspoons of the remaining oil in the skillet. Crack three of the eggs into the skillet and fry them until the whites are firm but the yolks are runny. transfer them to a plate, season with salt and pepper, and repeat with the last three eggs.
When the tostadas some out of the oven, top each one with a fried egg, and let everyone top their tostadas as they wish.