How to Make It
Heat butter in a large Dutch oven over medium-high until foamy. Add chicken and cook, turning occasionally, until browned on both sides, about 8 minutes. Remove from pan; let stand 5 minutes. Cut into bite-size pieces and set aside.
Add mushrooms, shallots, and thyme to Dutch oven; cook, stirring often, until slightly browned, about 7 minutes. Add sherry; cook until reduced by about half, about 1 minute.
Whisk together flour and 1 cup stock; stir into sherry mixture. Add remaining 5 cups stock, rice, carrot, celery root, and salt. Cover and increase heat to high; bring to a boil. Reduce heat to medium-low; simmer until vegetables are just tender, about 40 minutes. Add chicken and green beans; simmer until beans are crisp-tender, about 5 minutes. Add cream and pepper.
Ladle soup into bowls. Drizzle evenly with oil, and sprinkle with cheese.