Bring a large pot of water to a boil.
Season generously with salt, then add half of the lemon zest and the lemon slices.
Add angel hair pasta and cook according to package instructions (about 3–4 minutes) until al dente.
Reserve ¾–1 cup pasta water, then drain and set aside.
In a large skillet over medium heat, melt the butter with the olive oil.
Add garlic and cook for 30–60 seconds until fragrant.
Stir in remaining lemon zest and lemon juice. Let simmer for 1–2 minutes.
Pour in the heavy cream and let it gently simmer for 2–3 minutes until slightly thickened.
Stir in the peas and cook for 2–3 minutes until warmed through and bright green.
Add the cooked pasta to the skillet.
Pour in ½ cup reserved pasta water and toss to combine.
Add Parmesan, salt, pepper, and red pepper flakes.
Continue tossing until the sauce is silky and coats the pasta, adding more pasta water as needed.
Remove from heat and stir in fresh parsley.
Taste and adjust seasoning as needed.
Serve immediately with extra Parmesan and a squeeze of fresh lemon juice.