Prep the Grill or Oven: Preheat your grill or oven to medium-high heat (about 350°F or 175°C).
Grill the Zucchini: Slice the zucchinis into thin strips. If grilling, drizzle them lightly with olive oil, and season with salt and pepper. Grill the strips until they are tender and have grill marks, about 3-4 minutes per side. If using the oven, roast the zucchini on a baking sheet for about 15 minutes until soft.
Sauté the Spinach: While the zucchini is grilling, heat olive oil in a skillet over medium heat. Add minced garlic and sauté until fragrant, about 1 minute. Toss in the spinach and cook until wilted, roughly 2-3 minutes. Season with salt and pepper.
Prepare the Cheese Mixture: In a bowl, combine ricotta cheese, half of the mozzarella, grated Parmesan, salt, and pepper. Mix well until creamy.
Assemble the Lasagna: In a baking dish, layer the ingredients starting with a layer of grilled zucchini on the bottom. Follow with half of the ricotta cheese mixture, half of the sautéed spinach, and a sprinkle of the remaining mozzarella. Repeat these layers again, finishing with a layer of zucchini on top.
Bake: Cover with foil and bake in the preheated oven for 20 minutes. Remove the foil and bake for an additional 10 minutes until the top is golden brown and bubbly.
Garnish and Serve: Allow the lasagna to cool for a few minutes, then garnish with fresh basil before serving.