Heat the olive oil and the butter in a large skillet. Add the onions and cook over low heat, stirring often, until caramelized and browned, about 30 minutes.
Transfer to slow cooker pot, and add the garlic, thyme, salt, pepper, and broth. Cover and cook over low heat for 6-8 hours.
Before serving, toast the bread and preheat broiler to high heat. Ladle the soup in and lay a slice of cheese over each bowl. Broil until the cheese is well browned and serve.