Heat a large pot of water for pasta noodles and cook according to package directions. (Reserve 1/2-1 cup pasta water to thin Alfredo sauce as desired)
To the same pot of water used to boil noodles, add shelled peas and cook for 2 minutes. Drain the peas and immediately transfer to a bowl of ice water to stop the cooking and preserve their bright green color.
While the pasta and peas cook, heat 1 Tbsp olive oil over medium high heat in a large, deep skillet.
Season chicken breast cutlets on both sides with salt and pepper. Sear in hot pan for 5-7 minutes per side, or until browned and cooked through. Remove and set aside.
Add butter and garlic, sautéing for 1 to 2 minutes until fragrant. Add the heavy cream and scrape the brown bits off the bottom of the pan from the chicken. Bring to a light simmer and add the parmesan to slowly melt into the sauce. Season with salt and pepper.
Slice chicken and add to the sauce, as well as the cooked peas to warm through. Finally add the pasta, along with reserved pasta water as needed to thin the sauce. Garnish with parmesan cheese.
