Pat chicken breasts dry with paper towels. Optionally slice each breast in half horizontally for quicker cooking. Season both sides with kosher salt and black pepper.

Heat a large skillet over medium-high. Add 3 tablespoons olive oil. When shimmering, place the chicken in the pan without crowding. Sear 8–10 minutes per side for whole breasts, or 3–5 minutes per side for halved breasts, until golden.

Transfer the seared chicken to a plate and set aside.

Reduce heat to medium-high and add a splash of the sun-dried tomato oil or 1 tablespoon olive oil. Add the grated garlic and sauté until just golden and fragrant, about 30–45 seconds.

Pour in 3/4 cup chicken broth to deglaze the pan, scraping any browned bits from the bottom.

Stir in 2/3 cup heavy cream, 1/2 cup chopped sun-dried tomatoes, 1/4 cup chopped basil, 1 teaspoon dried thyme, 1/2 teaspoon dried oregano, 1/3 cup grated Parmesan, and 1/3 teaspoon chili flakes. Mix until smooth and starting to thicken.

Return the chicken to the skillet, nestling it into the sauce. Cover and simmer over medium-low for about 8–10 minutes until the internal temperature reaches 165°F.

Remove the lid, spoon sauce over the chicken, and garnish with chopped basil or parsley and extra Parmesan. Serve immediately.