Pat the chicken breasts dry with paper towels, then season both sides generously with salt and pepper.
Place the flour in a shallow bowl. Dredge each chicken breast in the flour, turning to coat evenly and shaking off any excess.
In a large nonstick or cast-iron skillet, melt the butter with the olive oil over medium-high heat.
Add the chicken breasts and cook for 4-5 minutes per side, or until golden brown and nearly cooked through. Transfer the chicken to a plate and cover loosely with foil to keep warm.
Reduce the heat to medium. Add the garlic to the same skillet and sauté for 30 seconds, just until fragrant.
Pour in the chicken stock and use a wooden spoon to scrape up any browned bits from the bottom of the pan.
Stir in the heavy cream, oregano, thyme, and red pepper flakes. Bring the mixture to a gentle simmer and cook for 5-7 minutes, stirring occasionally, until the sauce begins to thicken slightly.
Gradually stir in the Parmesan cheese until melted and the sauce is smooth.
Add the sun-dried tomatoes to the pan, then return the chicken and any juices to the skillet. Simmer gently over medium-low heat for 5-6 minutes more, or until the sauce is thick, creamy, and the chicken is cooked through to an internal temperature of 165°F.
Taste and adjust seasoning with additional salt and pepper as needed. Garnish with fresh basil and extra Parmesan before serving.