Cook the Spaghetti: Bring a large pot of salted water to a boil. Add the spaghetti and cook according to the package instructions until al dente. Reserve 1 cup of the pasta cooking water, then drain the spaghetti and set it aside.
Sauté the Garlic: While the pasta is cooking, heat the olive oil in a large skillet over medium heat. Add the thinly sliced garlic and sauté until it turns golden brown and becomes fragrant, about 2-3 minutes. Be careful not to burn the garlic as it can become bitter.
Add Red Pepper Flakes: Stir in the red pepper flakes and cook for an additional 30 seconds.
Combine Pasta and Sauce: Add the drained spaghetti to the skillet with the garlic and oil. Toss the pasta to coat it evenly with the oil and garlic. If the pasta seems dry, add a little of the reserved pasta water, a tablespoon at a time, until you reach the desired consistency.
Season and Garnish: Remove the skillet from heat. Stir in the chopped fresh parsley and season with salt to taste. If desired, sprinkle with lemon zest for a fresh, zesty flavor.
Serve: Serve the Spaghetti Aglio e Olio hot, topped with grated Parmesan cheese if desired.