In a medium saucepan combine chicken broth and uncooked wild rice. Bring to boiling. Reduce heat and simmer, covered, for 40 minutes. Stir in green onions and cook for 5 to 10 minutes more or until rice is tender.
Combine half-and-half or light cream, flour, thyme, and pepper. Stir into rice mixture along with mushrooms. Cook and stir until thickened and bubbly. Cook and stir for 1 minute more. Stir in sherry and heat through. Makes 4 side-dish servings.