Preheat oven to 350°F (175°C). Butterfly chicken breasts.
Melt butter in an oven-safe skillet. Add garlic, oregano, and thyme; sauté until fragrant.
Add chicken and cook 3–4 minutes per side until golden.
Pour in 1/4 cup chicken broth and bake for 15 minutes until cooked through. Remove chicken and reserve pan juices.
Cook bacon until crispy; drain and chop. Cook pasta according to package directions; drain.
Place skillet over medium heat. Whisk in flour, remaining broth, Parmesan, and cream until thickened.
Stir in sun-dried tomatoes, red pepper flakes, and salt. Add bacon and return chicken to skillet. Simmer briefly.
Serve chicken and sauce over warm pasta.