Slice each chicken breast in half horizontally to make 4 thin cutlets, or use 4 cutlets. Place between plastic wrap and pound to even thickness; pat dry.
In a shallow dish, whisk together the flour, kosher salt, black pepper, and garlic powder. Dredge each cutlet in the flour mixture, shaking off excess.
Heat the olive oil and butter in a large skillet over medium heat until the butter melts. Add the chicken in a single layer (work in batches if needed) and cook 3–4 minutes per side until golden and nearly cooked through. Transfer to a plate and tent with foil.
If the skillet is dry, add 1/2 tablespoon olive oil. Add the minced garlic and sauté about 30 seconds until fragrant.
Pour in the chicken stock and scrape up any browned bits from the pan to deglaze.
Add the heavy cream, chopped sun-dried tomatoes, dried oregano, dried thyme, and crushed red pepper flakes (if using). Bring to a simmer over medium-high heat, then reduce to low.
Whisk in the grated Parmesan until melted and the sauce is smooth. Taste and adjust seasoning with salt and pepper as desired.
Return the chicken and any juices to the skillet, spooning sauce over each piece. Simmer 3–4 minutes until the chicken is warmed through and reaches 165°F (74°C).
Remove from heat and serve topped with sliced basil ribbons, if using.