Preheat a 12-inch non-stick skillet over medium-high heat.
Dab the chicken on all sides dry with paper towels.
Sprinkle the flour, Italian seasoning, and desired amount of salt and freshly ground black pepper over the chicken. Toss well to evenly coat.
Add 1 Tbsp of olive oil and 1 Tbsp of butter to the skillet. The butter should melt quickly.
Set the chicken in the skillet in an even layer, allowing space between each piece.
Let cook until golden brown on the bottom, about 3 minutes, then flip and cook for 2 minutes longer or until nearly cooked through.
Add remaining 2 Tbsp of butter, along with garlic and parsley. Cook for 1 minute longer.
Serve immediately.