Feel free to use any cheeses for a different take on this monster cheese lasagna. Slideshow: More Lasagna Recipes
Preheat the oven to 375°F.
In a large heavy pot, heat the oil over medium high heat until hot. Stir in the onion, garlic, 1 teaspoon salt and 3/4 teaspoon pepper, and cook, stirring, until golden, about 8 minutes. Stir in the flour and cook, stirring, 1 minute. Whisk in the milk and bring to a boil, whisking. Boil 5 minutes, then remove from the heat and stir in the mozzarella and asiago cheese until they are melted. Season the cheese sauce with salt and pepper to taste.
In a 3-to 3 1/2-quart lasagna dish spread 1 cup of the cheese sauce over the bottom. Place 3 lasagna noodles evenly over the sauce, leaving even space between the noodles. Top the noodle layer evenly with a layer of cheese sauce, then place another 3 noodles on top.
Spread an even layer of cheese sauce over the noodles, then dollop half the ricotta. Top with another layer of 3 noodles, then sauce, then the remaining 3 noodles and sauce. Dollop with the remaining ricotta and sprinkle with the cheddar cheese.
Cover the lasagna dish with aluminum foil and bake until the filling is bubbling, about 45 minutes. Uncover the dish and continue to bake until the cheese is browned, about 30 minutes more. Let the lasagna stand 10 minutes before serving.