Using paper towels, thoroughly pat the chicken breasts dry to ensure better browning. Cut them into evenly sized 1-inch cubes on a clean cutting board.
In a medium bowl, mix the flour, oregano, basil, paprika, salt, and pepper until well combined. Add the chicken pieces and toss gently with your hands or tongs until each piece is evenly coated with the flour mixture.
Place a large cast iron skillet over medium-high heat. Add the olive oil and 1 tablespoon of butter, swirling to coat the pan. When the butter is melted and starts to bubble (but not brown), carefully add the chicken pieces in a single layer, making sure they don't touch each other.
Let the chicken cook without moving it for exactly 3 minutes - this helps develop a golden-brown crust. Using tongs, flip each piece and cook for another 2 minutes on the second side.
Reduce heat to medium. Add the remaining 2 tablespoons of butter and minced garlic to the pan. Once the butter melts, sprinkle in the fresh parsley. Stir everything gently to coat the chicken pieces, and cook for 1 minute more, or until the chicken is no longer pink in the center when cut open.