Slice each well-washed stem vertically into two pieces. Blanch for 5 minutes in boiling salted water, drain, then simmer in a heavy pan with olive oil or butter. Grate some pecorino sardo or parmesan over the fennel while it is cooking, then turn the pieces and sprinkle with more of the same. Both sides should brown. This takes about 15 minutes. Add some pomodori appesi, which are small, and cook for another few minutes. Serve on its own.