Preheat the broiler. Halve the poblanos lengthwise and remove the stems and seeds. Place cut-side down on a baking sheet and broil until browned in spots, about 5 minutes. Transfer to a bowl, cover with a plate and set aside 5 minutes. Peel off the skin with your fingers, then cut the peppers into 1-inch strips.

Melt 2 tablespoons butter in a medium heavy saucepan over medium heat. Add 2 minced garlic cloves and saute 1 minute. Mix in the corn and saute 5 minutes. Stir in the cream and thyme, reduce the heat to medium low and cook 5 minutes to let the flavors incorporate. Turn off the heat and let cool slightly, then transfer to a blender and puree until smooth. Add 1/4 teaspoon salt, and pepper to taste.

Preheat the oven to 350 degrees F. Heat the remaining 2 tablespoons butter in a medium heavy skillet over medium heat. Add the onion and saute until translucent, about 5 minutes. Add the remaining minced garlic clove and cook 1 minute. Mix in the zucchini and poblano strips and cook 5 minutes; season with salt and pepper.

Spread about one-quarter of the corn mixture in the bottom of an 8-by-11-inch baking dish. Cover with 3 lasagna sheets. Layer one-quarter each of the poblano mixture and cheese over the pasta. Repeat the layering 3 more times. Cover with aluminum foil.

Bake until the pasta is tender, about 50 minutes. Turn on the broiler. Remove the foil and broil until golden brown and bubbly, 8 to 10 minutes. Let stand 15 minutes before serving.

Photograph by Johnny Miller