Bring a pot of salted water to a boil and cook the rigatoni until al dente according to package instructions; drain and set aside.
Heat 2 tablespoons of olive oil in a large skillet over medium-high heat.
Add the minced garlic, crushed red pepper flakes, and black pepper to the skillet and cook, stirring, for 2–3 minutes until fragrant.
Add the thinly sliced chicken and the salt; cook, stirring occasionally, until the chicken is cooked through, about 3–4 minutes.
Pour the marinara sauce over the chicken and stir to combine, then add the heavy cream and stir until smooth.
Bring the sauce to a simmer and cook for about 10 minutes to thicken slightly.
Add the butter and peas to the sauce and stir until the butter melts and peas are heated through.
Toss the cooked rigatoni into the sauce until evenly coated.
Serve topped with freshly grated Parmesan and an extra pinch of crushed red pepper flakes if desired.