Pat the chicken breasts dry with paper towels. Season both sides generously with kosher salt and black pepper.

In a large skillet, heat 2 tablespoons olive oil over medium-high heat. Place the chicken in the skillet and cook for 5-6 minutes per side, until golden brown and cooked through (internal temperature reaches 165°F). Transfer to a plate and set aside.

Reduce heat to medium. Add the remaining 1 tablespoon olive oil to the skillet (or use 1 tablespoon oil from the sun-dried tomato jar). Add the minced garlic and sauté for about 30 seconds, stirring constantly, until fragrant.

Pour in the chicken broth, heavy cream, dried thyme, dried oregano, red pepper flakes, and sun-dried tomatoes. Stir to combine. Bring to a gentle simmer, then stir in the grated Parmesan and chopped basil until the cheese is melted and the sauce is smooth.

Return the cooked chicken to the skillet, spooning the sauce over the top. Cover and let simmer over medium-low heat for 5-7 minutes, until the chicken is heated through and the sauce has thickened slightly.

Garnish with additional fresh basil or parsley. Serve immediately over pasta, rice, or with crusty bread to soak up the sauce.