Preheat a 12-inch non-stick skillet over medium-high heat.
Dab chicken on all sides dry with paper towels.
Sprinkle flour, Italian seasoning, and desired amount of salt and pepper (I use about 1 scant tsp salt and 1/2 tsp pepper) over chicken. Toss well to evenly coat (all flour should stick to chicken and not be left behind on cutting board, keep tossing if needed).
Add 1 Tbsp olive oil and 1 Tbsp butter to skillet, butter should melt quickly. Tilt pan to evenly coat.
Add chicken in an even layer, work to leave some space between pieces so they'll brown rather than steam.
Let cook until nicely golden brown on bottom, about 3 minutes then flip to opposite side and cook 2 minutes longer, or until nearly cooked through.
Add remaining 2 Tbsp butter in small pieces, along with garlic and parsley. Cook 1 minute longer (chicken should be 165 in center and no longer be pink).
Serve right away.
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