Bring a large pot of salted water to a rolling boil. Add the pasta and cook until al dente, about 8-10 minutes, then reserve a cup of pasta water and drain the rest.
While the pasta cooks, heat 2 tablespoons of olive oil in a large skillet over medium heat until shimmering. Add the minced garlic and sauté for about 30 seconds until fragrant and golden, being careful not to burn it.
Add the fresh peas to the skillet and cook for 2-3 minutes until they start to pop and become tender. If using frozen peas, toss them in directly from the freezer and cook until heated through, about 2 minutes.
Stir in the chopped spinach and cook for another 1-2 minutes until wilted and bright green. If using mature spinach, chop it roughly beforehand and cook a little longer until tender.
Add the drained pasta to the skillet with the greens and peas. Toss everything together, adding a splash of the reserved pasta water gradually to create a silky, coating sauce. Cook together for about 1 minute to meld the flavors.
Remove the skillet from heat and squeeze in the lemon juice. Drizzle with the remaining tablespoon of olive oil, then toss again to distribute evenly. Season generously with salt and freshly cracked pepper to taste.
Serve immediately, garnished with extra lemon or grated cheese if desired. The pasta should be warm, bright, and coated with a light, flavorful sauce with peas bursting and greens tender but vibrant.
