Place 1 1/2 pounds chopped boneless chicken in a large bowl, add 3/4 teaspoon kosher salt and 1/4 teaspoon black pepper, and toss to coat.
Melt 2 tablespoons of the unsalted butter in a large cast iron or stainless steel skillet over medium heat. Add half of the chicken in a single layer. Cook until golden-brown and the chicken easily releases from the bottom of the pan, about 4 minutes. Toss and cook until golden-brown on the second side and cooked through, about 2 minutes more.
Transfer the chicken to a plate. Melt 1 tablespoon of the unsalted butter in the skillet and repeat cooking the remaining chicken. Transfer to the same plate.
Reduce the heat to low. Add the remaining 1 tablespoon unsalted butter, 3 minced garlic cloves, chicken, and any accumulated juices on the plate to the skillet. Cook until the butter melts and the garlic is fragrant, about 1 minute. Remove the skillet from the heat, add 1 ounce grated Parmesan cheese, and toss to coat. Garnish with 1 teaspoon finely chopped fresh parsley, more Parmesan cheese, and red pepper flakes if desired.
