Preheat a 12-inch nonstick skillet over medium-high heat.
Pat the chicken pieces dry with paper towels.
In a bowl, toss the chicken with the all-purpose flour, Italian seasoning, and salt and pepper until evenly coated.
Add 1 Tbsp olive oil and 1 Tbsp butter to the hot skillet and tilt to coat the pan as the butter melts.
Arrange the coated chicken in a single layer with some space between pieces and cook undisturbed until golden on the bottom, about 3 minutes.
Flip the pieces and cook about 2 minutes more, until nearly cooked through.
Add the remaining 2 Tbsp butter in small pieces, then add the minced garlic and chopped parsley; cook and stir for about 1 minute, until garlic is fragrant and chicken reaches 165°F and is no longer pink.
Serve immediately.