Heat a 12-inch nonstick skillet over medium-high heat.
Pat the chicken pieces thoroughly dry with paper towels. This helps them brown instead of steaming.
Place the chicken in a bowl and sprinkle with the flour, Italian seasoning, salt, and black pepper. Toss until every piece is evenly coated and no loose flour remains.
Add the olive oil and 1 tablespoon of butter to the hot skillet. Allow the butter to melt, then gently tilt the skillet so the fat evenly coats the surface.
Arrange the chicken in a single layer, leaving a little space between the pieces. Cook for about 3 minutes without moving them, allowing the bottoms to become nicely golden.
Turn the chicken pieces and cook for another 2 minutes, or until they are almost cooked through.
Reduce the heat slightly. Add the remaining 2 tablespoons of butter along with the minced garlic and chopped parsley.
Cook the Garlic Butter Chicken Bites for about 1 additional minute, gently tossing them in the melted garlic butter until evenly coated. The chicken should reach an internal temperature of 165°F (74°C).
Remove from the heat and serve immediately while the chicken is hot and juicy.