Slice and Pound: Slice each breast horizontally into two cutlets, then pound to an even ½ inch. Pat completely dry with paper towels.
Season and Dredge: Whisk the flour, salt, pepper, garlic powder, paprika, and oregano in a shallow dish. Coat each cutlet and shake off the excess.
Heat the Skillet: Warm 1 tablespoon oil and 1 tablespoon butter in a 12-inch skillet over medium-high heat until the butter foams and the foam begins to settle.
Sear the Chicken: Cook 2 cutlets at a time for 3 to 4 minutes per side, until deep golden and 165°F (74°C) inside. Add the remaining oil for the second batch, then set the chicken aside.
Cook the Garlic: Reduce heat to medium, melt 1 tablespoon butter, and stir in the garlic for 30 seconds until fragrant but not browned.
Deglaze the Pan: Add the broth and lemon juice, scraping up the browned bits. Simmer 3 to 4 minutes until reduced by about one third.
Finish the Sauce: Stir in the cream and remaining 1 tablespoon butter. Simmer 1 to 2 minutes until glossy and it coats the back of a spoon.
Combine and Serve: Return the chicken to the pan, spoon the sauce over it for 1 to 2 minutes, then top with parsley and serve hot.