Melt butter over medium heat in a large saucepan or dutch oven. Add the mushrooms and onions and cook until the onions are translucent—about 5 minutes.
Add the chicken stock, thyme, barley, salt and pepper. Bring to a boil then reduce heat to low. Cover and simmer for 20-30 minutes or until barley is cooked.
Mix the flour and water well so there are no lumps. Slowly stir into the hot soup (mixture will be very thick). Cook, stirring frequently, for 2 minutes to cook the flour.
Slowly stir in the half-and-half and heat through. Remove thyme sprigs (if using fresh) before serving. Add any additional salt and/or pepper if needed.
Notes
Vegetable or mushroom stock may be substituted.Half-and-Half is an American concoction but you can make it yourself by mixing 1 part whole (full-fat) milk and 1 part single cream (close substitute to American "light cream")