Bring a large nonstick pot of salted water to a boil and cook the tortellini according to package directions; drain and set aside, reserving a little pasta water if desired.
In a small bowl, mix paprika, Italian seasoning, salt, and pepper.
If marinating chicken: drain buttermilk and pat chicken dry; otherwise, cut chicken into even bite-sized pieces and pat dry with paper towel.
Toss the chicken pieces with the seasoning mix, then sprinkle the flour over them and stir until evenly coated.
In the same nonstick pot (or a large skillet), heat 3 tablespoons reserved sun-dried tomato oil (or olive oil) over medium heat for about 30 seconds.
Add a basil sprig and the minced garlic and cook, stirring, about 30 seconds until fragrant; remove the basil sprig before chicken finishes cooking.
Add the coated chicken to the pan and cook over medium heat, stirring occasionally, until no longer pink inside; add more oil if needed.
When the chicken is nearly cooked, add the chopped sun-dried tomatoes and sauté until the chicken is fully cooked through.
Return the drained tortellini to the pot with the chicken, reduce heat to low, and gently stir for 1–2 minutes to combine.
Stir in the basil pesto and 1–2 tablespoons of the reserved sun-dried tomato oil to taste; season with additional salt, pepper, and red pepper flakes if desired.
Serve garnished with fresh basil and grated Parmesan if using.
