Clean fennel bulbs and discard the stalks and tough outer layers. Slice bulbs thinly, then chop finely. Place in a saucepan with oil and cook over low heat for 10 minutes. Pour in broth, season with salt and pepper, and bring to a simmer. Simmer for 30 minutes.
Sprinkle with chopped parsley and serve. Serves 4 to 6.