In a food processor, blend basil leaves, 1 cup veggie broth, 1/2 cup olive oil, garlic, lemon juice, and zest.
Fill a large pot with lightly-salted water, and bring to a rolling boil.
Heat 2 tablespoons olive oil in a large saucepan over medium heat. Add leek, green onion and broccoli, cook until softened, stirring occasionally – about 5 minutes.
Stir in 1 cup of broth and peas; bring to a simmer and cook for 5 minutes. Add asparagus and continue cooking until asparagus is soft, about 3 minutes more.
Stir fettuccine into pot of boiling water, bring back to a boil, and cook pasta over medium heat until cooked through but still firm to the bite, about 8 minutes. Drain.
Pour 1/4 cup basil-garlic mixture into pea mixture and cook and stir until heated through, about 1 minute. Remove from heat. Place pasta in a large bowl; pour veggies over pasta and top with remaining basil-garlic mixture. Sprinkle with Parmesan cheese.