Corn and Poblano Lasagna

INGREDIENTS

• 4 tablespoons unsalted butter, divided
• 12 (7 by 3-inch) no-boil lasagna sheets
• 4 poblano chiles, charred, peeled, stemmed, seeded and cut into 1-inch strips
• 1 teaspoon fresh thyme
• Salt and freshly ground black pepper
• 2 cups fresh corn kernels (from about 2 ears), or frozen and thawed
• 3 cloves garlic, minced, divided
• 1/2 cup thinly sliced white onion
• 1 large zucchini, thinly sliced lengthwise
• 2 cups shredded Oaxaca cheese, or mozzarella
• 2 cups heavy cream