Preheat the oven to 350 degrees F.
Melt 2 tablespoons butter in a medium, heavy saucepan over medium heat. Add 2/3 of the garlic 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 cool slightly. Transfer to a blender and puree until smooth. Season with salt and pepper.
Heat the remaining 2 tablespoons butter in a small, heavy skillet over medium heat. Add the onions and saute until translucent, about 5 minutes. Add the remaining garlic and cook for 1 minute. Mix in the zucchini and poblano strips and cook for 5 minutes for the flavors to incorporate. Season with salt and pepper. Turn off the heat.
Spread about 1/4 of the corn mixture over the bottom of an 11 by 8-inch 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. Repeat the layering 3 more times. Cover with foil.
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, 8 to 10 minutes. Let stand for 15 minutes before serving.
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