Generously butter a 9”x13” baking dish. Bring salted water to a boil in a large pot. Cook the lasagna noodles per package instructions, or for 8 to 9 minutes, stirring them as they cook so they won’t stick. Drain and immediately lay them out them on an oiled baking sheet.
Set a rack in the middle of the oven and preheat to 375 degrees Fahrenheit.
Spread about 1/2 cup tomato sauce onto the bottom of the buttered baking dish. Place a layer of cooked lasagna noodles over the sauce, draping them so they coat the entire surface. Spread half the spinach and mushroom filling over the noodles.
Place a second layer of cooked lasagna noodles. Top with half of the poblano and corn mixture and half of the zucchini slices. Cover with about a cup of the salsa roja.
Place a third layer of cooked lasagna noodles. Top with the other half of the spinach and mushroom filling.
Place a fourth layer of cooked lasagna noodles. Add the remaining half of the poblano and corn mixture, the rest of the zucchini slices, and about a cup of the salsa roja.
Place fifth layer of cooked lasagna noodles and cover with the remaining cup of tomato sauce. Add the grated Oaxaca or mozzarella cheese, and top with the Cotija cheese or parmesano reggiano.
Cover the baking dish loosely with aluminum foil, making sure it is tight all around the edges, but that there is a lot of space over the cheese - like a tent or bubble - so the aluminum is not very close to the cheese on top.
Place baking dish on a baking sheet and put into the oven. Bake for 40 minutes, then carefully remove the aluminum foil and return to the oven for another 25 to 30 minutes. The top should have melted, browned and begun to crisp along the edges. Remove from the oven and let the lasagna sit for 10 minutes before cutting into it.