Melt the butter in a large pot over medium heat. Add the sliced onions and cook, stirring often, until they turn soft and golden brown, about 20 minutes.
Stir in the dried thyme, salt, and pepper. Pour in the beef broth and bring the mixture to a gentle simmer. Let it cook for 15 minutes so the flavors blend.
While the soup simmers, place the French bread slices on a baking sheet. Sprinkle the shredded Gruyère cheese evenly over each slice.
Broil the bread for 2 to 3 minutes until the cheese melts and turns lightly golden. Keep a close watch to avoid burning.
In a large bowl, toss the mixed salad greens and cherry tomatoes with the olive oil and balsamic vinegar.
Ladle the soup into bowls and top each with one slice of the Gruyère toast. Serve the side salad alongside.