Boil 6 cups of water in a large pot set over high heat and salt generously. Add the pasta and cook according to the package until al dente.: The sound of a vigorous boil is your first cue, a rolling noise that promises even cooking. Watch the water and add a generous pinch of kosher salt so the pasta absorbs seasoning as it cooks, resulting in a more flavorful dish overall. When you add the pasta you should hear a soft, rapid sizzle as the strands hit the water, and bubbles will momentarily splash. Stir immediately to prevent sticking, and check for al dente a few minutes before the package time by tasting a piece for a slight bite. A common mistake is underusing water, which causes the pasta to clump and cook unevenly, so use a spacious pot. Keep an eye on the clock and set a gentle timer to avoid overcooking, because once pasta becomes mushy it cannot be reversed.
While the pasta cooks, heat the butter and olive oil together in a large skillet set over medium-high heat. Add the asparagus and garlic. Stir and cook until the asparagus starts to soften, about 3 minutes.: You will hear a light sizzle when the butter and olive oil hit the warm pan, and that aroma tells you the pan is ready. Add the chopped asparagus and minced garlic , then stir so each piece gets coated with fat, which helps with caramelization and flavor development. The asparagus should take on a brighter green color and a slightly tender snap, and the garlic should smell fragrant and sweet rather than sharp. Keep the heat moderate to avoid charring the garlic, which leads to bitterness. Overcrowding the skillet can steam the asparagus rather than sauté it, so give the pieces room to brown a bit for deeper flavor.
Pour in one cup of the pasta water. Add the heavy cream, lemon juice, red pepper flakes, salt, and pepper and let it cook down until the pasta is ready.: When you ladle in reserved pasta water, you will see little bubbles form as the starchy liquid meets the warm skillet, and this helps the sauce thicken and cling. Adding the heavy cream next mellows the acidity of the lemon and creates a silky texture. Stir to combine and watch as the sauce reduces slightly into a glossy coating, carrying flecks of crushed red pepper flakes for warmth. The scent should be creamy with a lemon lift. If the sauce feels too loose, let it simmer gently, stirring often, until it lightly coats the back of a spoon. A typical pitfall is overheating the cream, which can break the sauce, so keep the temperature moderate and steady.
Drain the pasta and add it to the skillet. Toss to combine and sprinkle with Parmesan cheese. Serve with fresh parsley and lemon wedges.: After draining, when you add the pasta to the sauce you should see the noodles glisten as they pick up the creamy emulsion, and a soft sizzle may sound as moisture interacts. Toss gently with tongs or a pasta fork to ensure every strand has an even coating, and if needed add a splash more reserved pasta water to loosen the sauce for glossy coverage. The final sprinkle of freshly grated Parmesan will melt into the warm sauce and add a savory depth, while chopped parsley offers a fresh, herbal note. Plate immediately with lemon wedges so each diner can brighten their portion. A frequent mistake is letting the pasta sit too long before serving, which causes the sauce to clump and the texture to dull, so serve promptly while everything is warm and lively.