Add the pasta to a large pot of boiling salted water and cook until al dente (see package for instructions). Drain the pasta, reserving 1 cup of the pasta water. Set pasta aside.
Using the same pot, melt the butter over medium heat. Add the garlic and cook for 2-3 minutes. Add in the pasta and spinach. Gently toss and cook until spinach leaves are wilted. If the pasta starts to dry out, add in some of the reserved pasta water. You will typically need about 1/3 cup. Stir in 1/4 cup of the Parmesan cheese and toss until combined. Season with salt and freshly ground black pepper, to taste.
Transfer pasta into a large bowl. Garnish with additional Parmesan cheese and serve immediately.