Preheat the oven to 350 degrees F.
In a large heavy saute pan, add enough oil to come 2 inches up the sides of the pan. Heat the oil on medium-high heat. When hot, work in batches and quickly fry the tortillas for about 10 seconds on each side (they should still be pliable). Remove the tortillas from the heat and drain on a paper-towel-lined plate.
In a medium saute pan over medium heat, heat 2 tablespoons vegetable oil and add the garlic and onion. Saute until the onion is translucent, about 3 minutes. Add the tomato puree. Cook for 10 minutes and turn the heat off.
In a separate large saute pan over medium heat, melt the butter. Add the zucchini and corn. Cook for 2 minutes, and then add the chopped poblano chiles. Add 1/2 cup water to the mixture and cook for 4 more minutes. Season with salt and pepper.
Spray a 9-by-13-inch baking dish with a nonstick cooking spray. Cover the bottom with about 4 tortillas. Add 1/2 cup of the tomato mixture on top of the tortillas. Top with 1 1/2 cups of the zucchini mixture. Add 1 cup of the cheese. Drizzle with 1/4 cup of Mexican crema. Sprinkle the first layer with some salt and pepper. Start on the second layer with the tortillas, then the tomato, zucchini, cheese and Mexican crema. Again sprinkle with some salt and pepper. Repeat for a third time, to finish off a third layer. Place the casserole into the oven until the cheese is melted, 10 to 15 minutes. Serve hot.