Fill a large pot with water, add a generous pinch of salt, and bring to a rolling boil. Drop in your pasta and cook until just shy of al dente, about 1-2 minutes less than package instructions. Drain, reserving about a cup of pasta water, and set aside.
While the pasta cooks, trim the woody ends off the asparagus, then cut the spears into 2-inch pieces. Rinse the peas if fresh, or measure out frozen peas—no need to thaw.
Heat your wide skillet over medium-high heat and add two tablespoons of olive oil. When shimmering and fragrant, add the asparagus pieces and sauté until they turn bright green and are slightly charred around the edges, about 3-4 minutes.
Add the peas to the skillet and cook for another 1-2 minutes, stirring gently, until warmed through and slightly plump. If the pan gets dry, splash in a teaspoon of water or more oil.
Drain the pasta and add it directly into the skillet with the vegetables. Toss everything together with tongs, allowing the flavors to meld for about a minute. If needed, add a splash of the reserved pasta water for looseness.
Zest half of the lemon directly over the pasta to release its aromatic oils, then squeeze in the juice. Season generously with salt and pepper, tasting as you go. Toss again to combine everything evenly.
Sprinkle the freshly grated cheese over the pasta, stirring gently until it melts into a silky coating. Check the seasoning and adjust with more salt or pepper if needed.
Remove from heat and let sit for a minute so flavors settle. Serve immediately, garnished with extra cheese and a drizzle of olive oil if desired. Enjoy this bright, spring-inspired pasta!