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 3/4 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.
Notes
*For extra herb flavor double up on the parsley. For another layer of flavor you can finish by juicing in half a lemon.
Nutrition estimate based on 3 servings. Does not include added salt.
For a quick side I like to serve this with lemon couscous. To make it just bring 1 (14.5 oz) can chicken broth, 2 Tbsp lemon and 2 Tbsp water to a boil in a small saucepan. Once it boils, add 1 cup couscous (not pearl), then remove from heat, let stand 5 minutes. Fluff and serve.
I also love to serve it with sautéed or steamed vegetables for a quick meal (such as squash, zucchini, asparagus or broccoli).