Melt butter with oil in large pot over medium-high heat.
Add onions; sauté until soft and dark brown, about 20 minutes.
Add chicken broth, cider, and thyme sprigs. Bring to boil. Reduce heat; season with salt and pepper. Simmer soup, uncovered, 25 minutes. Discard thyme sprigs. (Soup can be made 1 day ahead. Cool slightly. Chill uncovered until cold, then cover and keep refrigerated. Rewarm over low heat before continuing.) Divide among 6 soup bowls, garnish with chopped thyme, and serve.