Bring a large pot of salted water to a boil. Add the package of cheese tortellini and cook according to package instructions, about 3 to 5 minutes, until tender and floating. Drain and set aside.
While the pasta cooks, heat 2 tablespoons olive oil in a large skillet over medium heat. Add minced garlic and sauté for about 1 minute until fragrant but not browned. Add chopped fresh spinach and cook until wilted, about 2 to 3 minutes.
Reduce heat to medium-low. Pour 1 cup heavy cream into skillet with garlic and spinach. Stir gently and bring to a low simmer. Gradually add grated Parmesan and shredded mozzarella, stirring until cheese melts and sauce thickens slightly. Season with salt, pepper, and nutmeg to taste.
Add drained tortellini to skillet and gently toss to coat with sauce. Cook for 1-2 more minutes to warm through and marry flavors.
Serve hot, garnished with extra Parmesan if desired. Enjoy your creamy, cheesy Cheesy Spinach Alfredo Tortellini!