Melt 2 tablespoons butter in a medium, heavy saucepan over medium heat. Add two-thirds of the garlic and the corn and saute for 5 minutes. Stir in the cream. 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 season with the thyme and some salt and pepper, and puree until smooth.
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 poblano strips and zucchini and cook for 5 minutes for the flavors to incorporate. Season with salt and pepper. Turn off the heat.
Spread about one-quarter of the corn mixture over the bottom of an 11-by-8-inch baking dish. Cover with a layer of 3 lasagna sheets. Spread one-quarter of the poblano mixture and one-quarter of the cheese over the pasta. Repeat the layering three 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.