Step 1: Slice each chicken breast in half horizontally into 4 even cutlets about 1/2 inch thick and pat dry. Mix the flour, salt, pepper, paprika, and garlic powder, then press each cutlet into it and shake off the extra until evenly dusted with no wet patches. Wash hands, knife, and board with hot soapy water afterward.
Step 2: Heat the olive oil and butter in a large skillet over medium-high heat until the butter foams. Sear the cutlets 4 to 5 minutes until the underside is deep golden and lifts easily, flip, and cook 3 to 4 minutes more until golden. Move to a plate.
Step 3: Lower the heat to medium. Add the garlic, sun-dried tomatoes, oregano, thyme, and red pepper flakes and stir about 1 minute until the garlic smells sweet and is pale gold, not brown.
Step 4: Pour in the stock and scrape up the browned bits with a wooden spoon. Simmer about 3 minutes until reduced by a third and the pan bottom looks clean.
Step 5: Add the cream and bring to a gentle simmer. Stir in the parmesan a handful at a time and simmer 4 to 5 minutes until the sauce coats the back of a spoon and holds a clean line.
Step 6: Return the chicken and its juices to the skillet and spoon sauce over it. Simmer on low 3 to 4 minutes until an instant-read thermometer in the thickest part reads 165°F (74°C) and the juices run clear. Top with basil and rest 2 minutes before serving.