Slice the chicken breasts horizontally in half to create four even cutlets. Pat them thoroughly dry with paper towels. In a shallow dish, whisk together flour, garlic powder, oregano, sea salt, and black pepper. Lightly dredge each cutlet, shaking off any excess.

Heat olive oil and butter in a large heavy skillet (cast iron or stainless steel) over medium-high heat until shimmering. Add the chicken cutlets in a single uncrowded layer and sear for 4 to 5 minutes per side until deeply golden brown and cooked through (internal temperature 165°F / 74°C). Transfer to a warm plate and tent loosely with foil.

Reduce the skillet heat to medium. Add the minced garlic and sliced sun-dried tomatoes to the remaining pan drippings. Sauté for 60 seconds until fragrant, stirring constantly to avoid scorching the garlic.

Pour in the chicken bone broth, using a wooden spoon to firmly scrape up all the golden browned bits (fond) from the bottom of the pan. Simmer for 2 to 3 minutes until the broth reduces by half.

Turn heat to medium-low. Pour in the heavy cream and red pepper flakes. Bring to a gentle simmer for 3 minutes until the sauce slightly thickens and coats the back of a spoon. Whisk in the freshly grated parmesan cheese until completely smooth and velvety.

Return the seared chicken cutlets and any rested juices back into the skillet. Spoon the warm sauce generously over the top and let simmer for 1 to 2 minutes until hot throughout. Remove from heat, scatter fresh basil ribbons on top, and serve immediately.