Prepare the pasta according to the instructions, saving ½ cup of the pasta water before draining. Do not rinse the pasta after draining.
Warm the oil in a large skillet over medium heat until shimmering, then add the garlic. Cook for about 30 seconds, until fragrant.
Add mushrooms, asparagus, pepper flakes, and 2 tablespoons of butter. Stir to coat the vegetables, then stir and cook for 3-4 minutes, until the mushrooms have softened and asparagus is bright green and slightly tender.
Add the cooked pasta and lemon juice to the skillet and season with salt and pepper to taste. Toss to combine and coat the pasta. Add a splash of the reserved pasta water, adding a touch more if the pasta is dry. Continue to toss the pasta until the sauce has emulsified, then stir in the remaining butter. Serve topped with cheese.