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