Cook the spaghetti in a large pot of boiling salted water until al dente, stirring occasionally, for about 8 minutes. While the spaghetti is cooking, using a large pan or skillet over medium heat, melt the butter. Continue to cook the butter until slightly browned and fragrant. Stir in the lemon zest and let cook for a minute.
Drain the pasta, reserving 1 1/2 cups of the pasta water. Pour 1 cup pasta water into the skillet with the lemon zest and add in the spinach. Mix together for a minute or two, and add in the cooked spaghetti and the parmesan cheese. Using tongs, toss together the pasta with the lemon sauce and the cheese. You shouldn't need to add anymore liquid because the spinach will also release some liquid but if you need to, add some more of the reserved pasta water. Add a squeeze of fresh lemon juice, season with salt and pepper, mix together and taste. Adjust anything if needed. Garnish with some fresh basil and serve with lemon wedges; you can also garnish with some lemon zest if desired. Enjoy immediately!