Preheat your oven to 400°F .
Heat a large heavy dutch over medium-high heat, and add the olive oil. Add the ground chicken to the oil, and season with salt and pepper. Cook, breaking up with the back of a wooden spoon and stirring every now and then, until the meat is cooked through and browned, about 15 minutes. Add the garlic, tomatoes, and season with salt and pepper. Stir to combine and scrape up any browned bits that are stuck to the bottom of the pot. Bring the mixture to a boil then lower the heat to a simmer, and cook the sauce for about 20 minutes until slightly reduced. Turn off the heat and set aside.
Cook the pasta until al dente. Drain the pasta, add it to the pot with the tomato sauce, and stir well to combine.
While the pasta is cooking, put the spinach, heavy cream, Parmesan, half of the mozzarella, and the basil leaves into a large bowl. Season with 1 tsp salt and 1/2 tsp pepper and stir well to combine.
Spoon one-third of the sauced pasta into a 9-by-13-in baking dish and spread into an even layer. Dot the pasta with half of the spinach mixture. Continue with half of the remaining pasta, all of the remaining spinach mixture, and then the final layer of pasta. Sprinkle the remaining mozzarella on top.
Bake the pasta, uncovered, until it golden browned and the edges are bubbling, about 30 minutes. Let it rest at room temperature for at least 15 minutes before serving.