Melt the butter in a large skillet over medium heat. Stir in the apple and onion; cook and stir until the onion has softened and turned translucent, about 10 minutes. Stir in the flour, chicken broth, and half-and-half, cooking until the sauce has thickened, about 5 minutes. Season with curry powder, salt, ground ginger, and cayenne pepper. Add the chicken, then cover and cook until the chicken is longer pink in the center, about 10 minutes.
