Bring Homemade Chicken Stock to a simmer in a small saucepan (do not boil). Keep warm over low heat.
Heat oil in a large saucepan over medium heat. Add shallots, onion, and thyme to pan; cook 5 minutes or until tender, stirring frequently. Add mushrooms; cook 1 minute. Add rice; cook 1 minute, stirring frequently. Stir in vermouth; cook 30 seconds or until liquid is nearly absorbed, stirring constantly. Stir in 1 cup stock; cook 4 minutes or until the liquid is nearly absorbed, stirring frequently. Add remaining stock, 1/2 cup at a time, stirring constantly until each portion of stock is absorbed before adding the next (about 25 minutes total). Add cheese, cream, salt, and pepper; cook 2 minutes. Remove from heat; top with chives.