Heat butter in a large Dutch oven over med-high heat. Brown chicken & remove from pan. Cool 5 minutes and slice into bite size pieces.
Add mushrooms, shallots and thyme to Dutch oven. Cook, stirring often, until browned, about 7 minutes. Add sherry and cook until reduced by half, about 1 minute.
Whisk together flour, 1 cup of stock and stir into the sherry mixture. Add remaining 5 cups stock, rice, carrot, celery root and salt. Cover and bring to a boil, then reduce heat to low to simmer and cook until the veggies are just tender - about 40 minutes. Add chicken, green beans and simmer til beans are crisp-tender - about 5 minutes. Stir it the cream and pepper.
To serve, drizzle with oil & sprinkle with cheese.