Cut the fennel tops where they meet the bulb and discard them. Check if the outer parts are damaged and discolored and if so remove them. Slice about 3 mm of the end. Cut the bulb vertically into slices of roughly 1 cm thick and wash them in cold water.
Put the fennel and the butter into a large saucepan, add just enough water to cover and turn the heat to medium. Don't cover. Let it cook very slowly for about 25-40 minutes. I added the rind of the parmesan to it which gave it an even cheesier taste.
If the liquid becomes too little in the pan you can add a little bit of water if needed. The end of the slice will be firmer than the top once cooked, but it should be soft enough.