Melt butter with olive oil in a large Dutch oven or soup pot on the stovetop over low to medium heat.
Add in onions and cook over heat 5- 10 minutes until onions are translucent (Do not brown onions.)
Add beef and chicken broths, apple cider and thyme sprigs.
Simmer soup uncovered on low for 30 minutes.
Remove thyme sprigs.
Season with salt and pepper
Ladle soup into individual, oven-safe serving bowls.
Float a slice of French bread on top of the soup in each bowl
Top with a slice of sharp Cheddar cheese.
Place bowls on a baking sheet and place in oven under broiler for a minute or two, or until cheese is bubbly and just turning golden. Watch carefully!
Remove from oven and serve immediately!