Bring a large pot of salty water to boil and cook pasta following package directions.
While pasta is cooking, cut asparagus into 1-inch pieces.
To a large pan, add asparagus and peas. Add about ½ inch of pasta water, cover, and bring to a boil. Cook over medium-high heat for about 3 minutes. Drain remaining water and return pan to stove.
Add olive oil, garlic, salt, and pepper to vegetables and saute for 2 minutes or until they are still crisp but tender. Remove from heat.
Reserve ½ cup of pasta cooking water, drain, and put pasta into pan with sauteed vegetables.
Add Parmesan, lemon zest, and half of the lemon juice and toss well to combine. Add a touch of pasta cooking water gradually and stir well to combine until pasta is nicely coated.
Serve immediately. Garnish with freshly grated Parmesan cheese and a drizzle of extra virgin olive oil.