Melt the butter in a stock pot over medium heat. Add carrots, onions, leeks, and celery. Cook and stir until tender, but not browned, about 10 minutes. Stir in thyme and mushrooms, and continue cooking until mushrooms are soft, about 5 minutes.
Pour chicken stock into the pot, and season with salt and pepper. Cover, and simmer over low heat for 30 minutes. Ladle into bowls, and serve with green onions sprinkled on the top.