Bring a large pot of salted water to a rolling boil. Add the pasta and cook until just al dente, about 8 minutes, stirring occasionally. Drain, reserving a cup of pasta water, and set aside.
While the pasta cooks, prepare the greens: trim the woody ends from the asparagus and cut into 2-inch pieces. Shell the peas if using fresh.
Heat the olive oil in a skillet over medium heat until shimmering. Add the asparagus tips and sauté for about 3-4 minutes until they develop a slight char and become tender yet crisp. Add the peas during the last minute of sautéing, just until heated through.
Drain the pasta and add it to the skillet with the greens. Toss gently to combine, adding a splash of reserved pasta water if needed to loosen the mixture and help the flavors meld.
Add the lemon zest and squeeze in the lemon juice, then sprinkle the minced garlic over everything. Toss again to evenly distribute the flavors, cooking for about 1-2 minutes until fragrant.
Stir in the freshly grated Parmesan cheese, and season with salt and pepper to taste. The dish should look glossy, vibrant, and inviting.
Remove from heat and let sit for a minute to allow the flavors to meld. Finish with a drizzle of olive oil and an extra sprinkle of Parmesan if desired.
Serve immediately while the greens are bright and the pasta is perfectly al dente, enjoying the lively flavors of spring in every bite.
