If using chicken breasts, cut each breast in half lengthwise and gently pound to make 6 thin cutlets. Season both sides of the chicken cutlets with kosher salt and freshly ground pepper to taste. Lightly coat each cutlet in the 6 tablespoons flour, shaking off any excess.

Heat a large skillet over medium-high heat and add the olive oil and butter to sauté (about 2 tablespoons each).

When the butter is melted and the pan is hot, add the floured chicken cutlets in a single layer (work in batches if they don’t fit without crowding). Brown the chicken 4–5 minutes per side, until golden and cooked through. Remove the cooked cutlets to a plate and cover with foil to keep warm.

Reduce the heat to medium. Add the minced garlic to the same pan and cook just until fragrant, stirring constantly (about 30 seconds).

Pour in the 1 cup chicken broth and scrape the bottom of the pan with a spoon to deglaze and release the brown bits. Bring the broth to a gentle simmer.

Reduce the heat to medium-low and stir in the 1 cup heavy cream and ½ cup grated Parmesan cheese. Simmer the sauce until it begins to thicken slightly, stirring so the cheese melts into the sauce.

Stir in ½ teaspoon red pepper flakes, ¼ teaspoon dried oregano, and ¼ teaspoon dried thyme. Taste the sauce and add kosher salt and freshly ground pepper as needed.

Add the ⅓ sun-dried tomatoes, chopped, to the sauce. Return the chicken cutlets to the pan, spooning sauce over them, and let everything simmer together for a few minutes until the chicken is heated through and the sauce coats the cutlets.

Garnish with chopped fresh basil if desired and serve.