Cook the pasta: Bring a large pot of salted water to a boil. Cook the spaghetti according to package instructions until al dente. Reserve 1/2 cup of the pasta water before draining.
Prepare the walnut sauce: In a large skillet, heat the olive oil over medium heat. Add the minced garlic and cook for about 1-2 minutes until fragrant, being careful not to burn it.
Add the walnuts: Stir in the chopped walnuts and cook for another 2-3 minutes, allowing them to toast slightly and release their natural oils.
Toss the pasta: Add the cooked spaghetti to the skillet, tossing to coat it in the garlic and walnut mixture. If the pasta seems dry, add a splash of the reserved pasta water to loosen the sauce.
Finish with Parmesan and parsley: Remove from heat and stir in the Parmesan cheese and chopped parsley. Season with salt and black pepper to taste.
Serve: Plate the pasta and sprinkle with additional Parmesan cheese and a drizzle of olive oil for extra flavor.