Heat a 12-inch non-stick skillet over medium-high heat.
Pat the chicken pieces dry with paper towels to remove any excess moisture.
Sprinkle the chicken with flour, Italian seasoning, and your desired amount of salt and pepper (approximately 3/4 tsp salt and 1/2 tsp pepper). Toss to coat evenly, ensuring the flour sticks to the chicken.
Add 1 Tbsp of olive oil and 1 Tbsp of butter to the skillet. Once the butter melts, tilt the pan to evenly coat the surface.
Add the chicken to the skillet in an even layer, making sure there's some space between each piece to allow for browning rather than steaming.
Let the chicken cook undisturbed for about 3 minutes until it turns golden brown on the bottom. Flip the pieces over and cook for an additional 2 minutes or until the chicken is nearly cooked through.
Add the remaining 2 Tbsp of butter, along with the garlic and parsley. Stir and cook for 1 more minute, until the chicken reaches an internal temperature of 165°F and is no longer pink in the center.
Serve immediately.