Roast the eggplant:Slice the eggplant into 1/2-inch slices (at least 12 planks; don’t worry if they vary in size). Place the slices on two parchment-lined baking sheets and brush each side with them with olive oil. Sprinkle with 1 teaspoon kosher salt, divided across the 2 trays. Roast for 10 minutes, then flip and bake 10 to 15 minutes more, until tender and golden brown.
Prepare the sauce:Mince the garlic. Add the butter to a medium saucepan over medium heat: once melted, add the garlic and sauté until fragrant, about 1 minute. Turn down the heat and carefully add the crushed tomatoes, tomato sauce, basil, tarragon, ½ teaspoon kosher salt, and several grinds of black pepper. Remove ¼ cup of the sauce and stir it with the cornstarch, then add it back to the pan (this helps to thicken the sauce). Simmer while making the remainder of the recipe, at least 15 minutes. When ready to use, remove the pan from the heat.
Meanwhile, prepare the cheese filling: Destem the thyme, then roughly chop the leaves. Add 2 tablespoons thyme to a medium bowl and reserve about ½ tablespoon for topping the lasagna. To the bowl, add the lemon zest, ricotta cheese, ½ cup Parmesan cheese, 1 cup shredded mozzarella cheese, nutmeg, ½ teaspoon kosher salt, and several grinds of black pepper. Stir to combine.
Turn down the oven: Turn down the heat to 375°F.
Assemble the lasagna: In a 9” x 9” baking dish or 7 x 11 baking dish (or similar volume dish), spread a ½ cup tomato sauce on the bottom of the pan. Then top with 1 layer of the eggplant, half of the cheese mixture (in dollops) and about ½ cup of the tomato sauce, using a spatula to spread the sauce evenly over the cheese. Repeat again, topping with 1 layer of eggplant, the remaining cheese mixture, and ½ cup of the remaining tomato sauce. Finally, top with a final layer of eggplant, then another ½ cup tomato sauce. Sprinkle the entire top with the remaining 1 cup mozzarella cheese, ¼ cup Parmesan cheese, and ½ tablespoon fresh thyme.
Bake the lasagna: Bake the lasagna for 30 minutes, uncovered. Let stand for at least 15 minutes before serving (this allows the lasagna to set; you can let it sit even longer if desired). Leftovers can be refrigerated for up to 3 days and reheated in a 375°F oven.