Pat the chicken breasts dry with paper towels. If they are very thick, slice them in half horizontally to ensure even cooking. Season both sides generously with kosher salt and black pepper.

In a large skillet (12-inch or larger), heat the olive oil over medium-high heat until shimmering. Add the chicken breasts and cook without moving them for 5-6 minutes, until a golden-brown crust forms. Flip and cook the other side for 5-6 minutes. The chicken should be cooked through (internal temperature 165°F). Transfer the chicken to a plate and set aside.

Reduce the heat to medium. Add a splash of the oil from the sun-dried tomatoes to the skillet, then add the minced garlic. Sauté for 30 seconds, stirring constantly, until fragrant and just golden.

Pour in the chicken broth and heavy cream, scraping up any browned bits from the bottom of the pan. Add the chopped sun-dried tomatoes, chopped basil, dried thyme, dried oregano, red pepper flakes, and grated Parmesan. Stir with a wooden spoon until the cheese melts and the sauce is smooth.

Return the cooked chicken to the skillet, spooning some sauce over each piece. Reduce the heat to medium-low, cover, and simmer for 5 minutes to let the flavors meld and the sauce thicken slightly.

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