Heat oil in a large deep skillet or pot over medium heat. Cook garlic about 1 minute until fragrant, not browned.
Add pasta, asparagus, and broth. Season with salt, pepper, and optional red pepper flakes; stir.
Bring to a boil over medium-high; reduce to medium. Cook uncovered 10-12 minutes, stirring frequently to prevent sticking, until pasta is nearly al dente.
Add peas; cook 2-3 minutes more until pasta is tender and most liquid absorbs.
Remove from heat; stir in cream, butter, lemon zest, and juice until butter melts and everything combines.
Stir in Parmesan and basil until cheese melts into creamy sauce. Adjust seasoning; serve immediately with extra Parmesan.