Heat olive oil in a large, deep skillet or pot over medium heat. Add the sliced garlic and cook for about 1 minute until fragrant but not browned.
Add the pasta, asparagus pieces, and broth to the pot. Season with salt, pepper, and red pepper flakes if using. Stir everything together.
Bring the mixture to a boil over medium-high heat. Once boiling, reduce to medium heat and cook uncovered for 10-12 minutes, stirring frequently to prevent sticking, until the pasta is nearly al dente.
Add the frozen peas and continue cooking for 2-3 more minutes until the pasta is tender and most of the liquid has been absorbed.
Remove from heat and stir in the heavy cream, butter, lemon zest, and lemon juice. Mix until the butter melts and everything is well combined.
Add the Parmesan cheese and torn basil leaves, stirring until the cheese melts into a creamy sauce. Taste and adjust seasoning as needed. Serve immediately with extra Parmesan on the side.