Bring a large pot of salted water to a boil. Add 12 ounces of cheese tortellini and cook according to package directions, about 3 to 5 minutes, until al dente. Drain and set aside.
Heat 1 tablespoon olive oil in a large skillet over medium heat. Add 1 teaspoon minced garlic and sauté for about 30 seconds until fragrant. Add 2 cups chopped fresh spinach and cook until wilted, about 2 to 3 minutes. Season lightly with salt and pepper. Remove from heat.
In a mixing bowl, whisk together 1 cup pesto sauce and 1 cup heavy cream until smooth and fully combined.
Add the cooked tortellini and sautéed spinach to the pesto cream sauce. Toss gently to coat evenly. Stir in 1 cup shredded mozzarella and 1/2 cup grated Parmesan cheese.
Transfer the mixture to a greased 9x13 inch baking dish and spread evenly. Sprinkle extra mozzarella and Parmesan on top if desired.
Bake in a preheated oven at 375°F (190°C) for 20 to 25 minutes, until the top is golden brown and sauce is bubbling. Let cool slightly before serving.