Melt 2 tablespoons of butter in a medium heavy saucepan over medium heat. Add 2 cloves of garlic (about 2 teaspoons) and saute for 1 minute. Mix in the corn and saute for 5 minutes. Stir in the cream and thyme. Cook over medium-low heat for 5 minutes for the flavors to incorporate. Turn off the heat and let it cool off a little bit. Transfer to a blender and puree until smooth (You can use an immersion blender for this step. I wish I had thought of that before right now.) Season with salt and pepper.

Turn on your broiler. Line a baking sheet with tin foil. Place the 4 peppers on the foil, then put it in the oven on the highest rack, as close to the heat as possible. Broil until the skin is mostly black. It should take 5 or 10 minutes, keep an eye on it. Then remove the pan from the oven, flip the peppers, and repeat on the other side. (Here is a great tutorial if you're nervous.) Place the peppers in a ziplock or in a covered bowl for 20 minutes to steam. Then carefully peel off the skins. Slit the peppers and discard the seeds and stems. Slice into 1-inch strips and set aside.

Heat the remaining 2 tablespoons of butter in a medium size skillet. Add the onions and saute until translucent, about 5 minutes. Add one clove of garlic and cook for 1 minute. Add in the zucchini and poblano strips. Cook for 5 minutes to allow the flavors to incorporate. Season with salt and pepper and remove from the heat.

Preheat the oven to 350 F.

Spread about 1/2 cup of the corn sauce over the bottom of an 11 by 8-inch (2-quart) baking dish. Cover with a layer of 3 lasagna sheets. Spread 1/4 of the poblano mixture and 1/4 of the cheese over the pasta. Then add another layer of noodles, then the poblano mixture, corn sauce, cheese. Repeat twice more. Noodles, poblano mixture, corn sauce, cheese. Top everything with crumbled queso fresco, if you want. (You want.)

Cover with foil that has been sprayed with nonstick spray. Place the casserole dish on a baking sheet in case it spills over.

Bake until the pasta is cooked and tender, about 50 minutes. Remove the foil and turn up the oven temperature to broil. Broil until golden brown and bubbly, 2 to 6 minutes. Keep an eye on it! Let stand for 15 minutes before serving.