Toss the thinly sliced chicken breasts in a bowl with olive oil, garlic powder, salt, smoked paprika, Italian seasoning, and black pepper until evenly coated.
Heat olive oil in a large skillet over medium-high heat. Cook the chicken for 3-4 minutes on each side until golden and cooked through (165°F internal temperature). Remove and set aside.
Cook rigatoni pasta in boiling salted water until al dente. Reserve 1/4 cup pasta water before draining the pasta.
In the same skillet, heat olive oil and 2 tablespoons butter over medium heat. Sauté shallot and garlic until soft and fragrant, about 2-3 minutes.
Add tomato paste and stir to combine, then pour in the passata, chopped Calabrian peppers, and vodka. Simmer for about 5 minutes until slightly reduced.
Season the sauce with salt, sugar, and Italian seasoning. Taste and adjust seasoning as needed.
Stir in heavy cream and simmer until the sauce thickens slightly. Optionally, use an immersion blender to blend the sauce smooth.
Add the drained pasta to the sauce along with reserved pasta water, 3 tablespoons butter, and grated Parmesan cheese. Stir until combined and creamy.
Slice the cooked chicken and serve it on top of or alongside the pasta. Garnish with fresh basil leaves and extra Parmesan cheese.