Bring a large pot of salted water to a boil and cook the pasta until al dente, following package instructions. Drain and set aside.
Heat a large skillet over medium heat, add a tablespoon of butter, and cook the chicken until golden brown and cooked through, about 5-7 minutes. Remove the chicken and set aside.
Add the remaining butter to the skillet, then stir in the minced garlic. Cook until fragrant, about 1 minute, and the mixture begins to smell aromatic.
Pour in the heavy cream, bringing it to a gentle simmer while stirring constantly. Let it cook for 2-3 minutes until slightly thickened.
Stir in the grated Parmesan cheese until melted and the sauce becomes smooth and creamy. Season with salt and pepper to taste.
Add the cooked chicken and thawed peas to the sauce, stirring to combine. Cook for another 2 minutes until the peas are heated through and the sauce is evenly colored.
Gently fold the cooked pasta into the skillet, tossing to coat thoroughly with the creamy sauce and evenly distribute the chicken and peas. Let everything warm together for a minute.
Serve the pasta hot, garnished with extra Parmesan cheese if desired, and enjoy the rich, creamy texture with bright pops of peas.