In a large pot, bring 4 quarts of water to a boil. Once boiling, add 1 tablespoon of salt.
Bring the water back to a boil and add the spaghetti noodles. Cook until al dente, about 11 minutes. Stir every few minutes to prevent sticking.
While the pasta is cooking, prepare the asparagus. Remove the tough ends and use a peeler to peel the asparagus lengthwise, creating long, thin strips resembling fettuccine noodles.
Heat a pan over medium-high heat. Once hot, add the olive oil and sliced garlic. Sauté for 1 minute, then add the red pepper flakes. Stir to combine.
Add ½ cup of the reserved pasta water to the pan. If needed, you can add more pasta water later. Add the cooked pasta and raw asparagus to the pan. Gently toss to combine.
Season with salt to taste. If the dish seems dry, you can add more pasta water to create a slightly saucy consistency.
Remove the pan from the heat and stir in half of the finely chopped fresh parsley.
To serve, plate the pasta and drizzle a generous amount of olive oil over it. Sprinkle freshly grated Parmesan cheese on top, and garnish with the remaining parsley.