Heat the oil in a large dutch oven over medium heat. Add onions and salt; cook, first tossing with tongs, and when they begin to wilt, stirring occasionally with a spoon, until pale golden brown and very soft, about 35 minutes.
Stir in the flour and cook, stirring occasionally, until the flour is lightly browned, about 2 minutes.
Transfer the onions to a 5 or 6 quart slow cooker. Add thyme sprigs and pepper. Pour the broth over the onions. Cover and cook until the flavors are blended 4-5 hours on high or 8-10 hours on low. Discard thyme sprigs when done.
Combine the cheese and thyme leaves in a bowl. Spread the cheese mixture over the bread slices. Ladle the soup into bowls, top each serving with a bread slice.