You can enjoy this dish slightly brothy, or lightly caramelized by continuing to simmer the fennel after it is tender until all the stock evaporates. If you are serving the fennel with a grilled piece of fish or meat, keep it nice and juicy. On the other hand, if you are serving the fennel as a contorno with a piece of meat or fish that has its own sauce, then cook off the liquid and serve the fennel dry.
Cut off the stalks flush with the tops of the bulbs. (Reserve the stalks for vegetable soup or boil and mash them along with potatoes. Save the leaves to flavor soups.)
Turn the bulbs cut side down and cut them into quarters through the cores. Remove the tough outer layers from the pieces, then cut out the cores. Slice the pieces crosswise into ¾-inch strips.
Heat the butter in a medium skillet over medium heat until foaming. Scatter the fennel pieces over the butter, season them lightly with salt and pepper and cook, tossing and stirring, until they begin to brown, about 6 minutes.
Pour in the chicken stock and bring to a boil.
Lower the heat so the stock is simmering. Cover the pan and cook until the fennel is tender, 15 to 20 minutes.
During the last few minutes, remove the lid from pan so about half the liquid evaporates.
If you’d like to serve the fennel ‘dry’ and lightly caramelized, continue cooking until all the liquid has boiled off the fennel is lightly browned, about 4 minutes.
Taste and add more salt and pepper if you like.