Use a sharp knife to slice the chicken breasts in half lengthwise. Season both sides with salt and black pepper.

Place the 1 tablespoon of butter in a large saucepan over medium heat, add the chicken breast and cook for about 5 minutes on each side or until cooked. Remove from the pan and set aside on a plate.

Add the rest of the butter, onion and garlic to the pan. Cook for about 2 minutes or until the onion is soft. Add the flour and cook for another 2 minutes, then add the milk to the flour mixture and whisk until the sauce thickens.

Place the cooked chicken breast in the sauce and cook for 1 more minute. Garnish with fresh chopped parsley and serve warm.

Stir in the cheese, stirring until the sauce is smooth. Season with salt and pepper to your taste.