Wash the fennel bulbs and remove the hard outer ribs, cut lengthways into 4-6 pieces. Blanch for about 5 minutes in boiling salted water, then drain.
Melt the butter in a shallow saucepan, add the fennel, season with salt and cook covered over low heat until al dente, but do not brown. Add 1/2 to 1 cup of cream spoon by spoon. It shouldn`t get too soupy. Finally, sprinkle the freshly grated cheese over the top and leave it covered until the cheese has melted.
Sprinkle with fresh, finely chopped fennel greens.