Heat the olive oil in a large deep frying pan on medium-high heat. Add the garlic and cook to soften, but not quite brown. Add the spinach and sauté with the garlic until wilted. Season with salt and pepper, remove from heat and set aside.
Cook the pasta according to package instructions. Reserve a cup of the pasta water before draining. Drain, and set aside.
Add the spinach and garlic mixture to a food processor or blender with the Parmesan cheese and half of the reserved pasta water. Puree until it forms a sauce (adding more pasta water if needed).
Add the sauce back into the pan to combine and heat through, again adding more pasta water if needed. Once heated through, taste and season with more salt and pepper, if necessary. Pour the sauce over the pasta and toss to coat evenly. Sprinkle with extra grated Parmesan cheese and serve.