Cook the pasta according to the package directions. Drain, reserving 1 cup of the cooking water. Return the hot pot to the stove.
Add the butter to the pot and melt over medium heat. Add the garlic and cook, stirring, for 2 minutes. Add the pasta back to the pot along with the spinach. Toss until the spinach wilts. (You may have to add the spinach in batches.) Add as much reserved cooking water as needed to keep the pasta moist. Add half the cheese and toss. Season to taste with salt and pepper. Serve the pasta topped with the remaining cheese.