Season the chicken cutlets with salt and pepper. Dredge each piece in flour and shake off any extra.
Heat the olive oil and butter in a large skillet over medium heat. Swirl the pan so the oil and butter coat the bottom evenly.
Add the chicken to the skillet. Do not overcrowd the pan. Cook in batches if needed. Brown the chicken for 4 to 5 minutes on each side, until golden and cooked through. Transfer to a plate, cover, and set aside.
In the same skillet, sauté the garlic for about 1 minute, just until fragrant. Pour in the chicken stock and scrape the bottom of the pan with a wooden spoon to loosen any browned bits.
Lower the heat to medium low. Add the heavy cream and grated parmesan cheese. Let the sauce gently simmer for a few minutes. Stir in the chili flakes, thyme, and oregano.
Season with salt and pepper to taste. Add the chopped sundried tomatoes. Return the chicken to the skillet and let everything simmer together for a few more minutes, until the sauce thickens and the chicken is coated.
Garnish with fresh basil and serve warm over pasta or rice.