Preheat the oven to 375°F. Bring a large pot of salted water to a boil and cook the lasagna noodles according to package directions until al dente. Drain and set aside.
Heat the olive oil in a skillet over medium heat. Add the minced garlic and cook for 30 seconds until fragrant. Add the chopped spinach, salt, pepper, and nutmeg. Stir until the spinach wilts, about 3 minutes. Remove from heat and let cool slightly.
In a mixing bowl, combine the ricotta cheese with the cooked spinach mixture. Stir until evenly blended.
Spread 1/2 cup marinara sauce across the bottom of an 8x8 baking dish. Lay 3 noodles over the sauce. Spread half the ricotta-spinach mixture on top, then sprinkle with 1/3 cup mozzarella. Repeat the layers once more.
Add the final 2 noodles. Spread the remaining marinara sauce over the top and sprinkle with the remaining mozzarella and all the Parmesan.
Reserve 2 tablespoons of marinara sauce. Pipe it in thin lines across the top to form a spiderweb pattern. Bake uncovered for 25 minutes until the cheese melts and bubbles at the edges. Let rest 5 minutes before slicing.