Preheat oven to 350°F (175°C).
Drizzle 2 tablespoons of olive oil over chicken breasts and rub in. Mix paprika, garlic powder, salt, and pepper, then sprinkle over chicken.
In a large, oven-safe skillet, heat the remaining olive oil over medium-high heat. Add chicken and sear for 3 minutes on each side. Transfer skillet to oven and bake for 10-15 minutes, until chicken reaches 165°F (74°C).
For pasta, cook rigatoni al dente as per package instructions. In the same skillet, melt butter over medium heat. Add shallots and sun-dried tomatoes, cooking until shallots are soft. Add garlic, cooking for an additional minute.
Stir in tomato paste, oregano, paprika, garlic powder, salt, and pepper. Add heavy cream and milk, stirring to combine. Add spinach, parmesan, and tomatoes, simmering until cheese melts and spinach wilts.
Toss cooked pasta in the sauce, then slice or cube chicken and add to the skillet. Serve garnished with parmesan and parsley. Season with salt and pepper to taste.