Bring a large nonstick pot of salted water to a boil and cook the tortellini according to package directions; drain and set aside.
If marinating, drain chicken from the buttermilk. Otherwise, cut chicken into even bite-sized pieces.
In a bowl, mix paprika, Italian seasoning, salt, and pepper. Pat chicken pieces dry with paper towels, toss with the seasoning mixture, then sprinkle and toss with the flour to coat.
Heat 3 tablespoons reserved sun-dried tomato oil (or olive oil) in the same large nonstick pot over medium heat. Add a basil sprig and the minced garlic and cook about 30 seconds until fragrant, then remove the basil sprig.
Add the seasoned, floured chicken to the pot and cook over medium heat, stirring occasionally, until no longer pink and cooked through; add more oil if needed.
When the chicken is almost done, add the chopped sun-dried tomatoes and sauté briefly until the chicken is fully cooked.
Return the drained tortellini to the pot with the chicken, reduce heat to low, and gently stir 1–2 minutes to combine.
Stir in the basil pesto and 1–2 tablespoons of the reserved sun-dried tomato oil as desired; taste and adjust seasoning with salt, pepper, and red pepper flakes if using.
Serve topped with fresh basil leaves and grated Parmesan if desired.