Melt 1 stick of butter in a large saucepan over medium heat.
Add the leeks, carrots, celery and sauté for 3 minutes or until tender. Sprinkle 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.
Purée 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.
Ladle the soup into bowls and garnish each serving with a sprinkling of finely chopped leeks.