Trim the fennels by cutting the stalks. Discard the hard outer skin. Blanch in boiling salted water for 20 to 25 minutes. Drain. Slowly brown in butter in a casserole. Cut the bacon into thin strips and blanch for 5 minutes in boiling water. Choose firm potatoes. Cut into large cubes. Fry the potato cubes in oil with the well wiped bacon. As soon as starting to brown, throw the contents of the frying pan over the fennel with the onions. Salt and pepper. Cover. Braise over a moderate heat until the potatoes and the fennel heads are soft, stirring from time to time. If the fennel heads are large, halve them after their first cooking.
