Bring the broth to a boil. In the meantime, heat the butter well and braise the bread slices (having removed the crusts and cut them in 2) until golden.
Put 2 halves at the bottom of each serving bowl, sprinkle with parmesan on top and carefully break an egg over each so that the egg yolk doesn't run.
Season with salt and black pepper, then pour on boiling broth. Serve the soup right away.