Melt 6 tablespoons of butter in a medium saucepan over medium heat. Add the leeks, carrot and celery and sauté until tender or about 3 minutes. Sprinkle the flour over the vegetables and stir for 3 minutes, making sure to cook the flour evenly.
Add the chicken stock slowly, whisking to evenly combine. Bring to a boil over medium heat, then reduce the heat and simmer uncovered for 40 minutes or until slightly thickened.
Puree the soup in a blender, food processor or with a handheld mixer. Strain into a clean saucepan. Bring to a simmer.
Add the half-and-half, cheese, mustard and Worcestershire sauce. Stir until the cheese is melted. Season to taste with salt, pepper and cayenne pepper. Keep warm.
Melt the remaining 2 tablespoons of butter in a small skillet. Saute the apple pieces until they start to turn golden brown and soft, about 3 minutes. Ladle the soup into bowls and garnish each serving with a large tablespoon of the sauteed apple mixture.