1. Remove roots, outer leaves, and tops from leeks. Cut leeks in half lengthwise. Rinse thoroughly with cold water, and cut each half into 1/4-inch slices.
2. Melt butter in a Dutch oven over medium heat. Add leeks, celery, and mushrooms; sauté 10 minutes or until tender. Stir in 6 cups broth. Add rice and next 3 ingredients (through pepper); bring to a boil. Cover, reduce heat, and simmer 45 to 55 minutes or until rice has "popped."
3. Weigh or lightly spoon flour into a dry measuring cup; level with a knife. Combine flour and 1 cup broth, stirring with a whisk until smooth. Add broth mixture to soup. Cook over medium heat 2 minutes or until slightly thick, stirring constantly. Reduce heat to low; add chicken, half-and-half, wine, and mustard. Cook 2 minutes or just until thoroughly heated (do not boil).