Rinse the chicory for about 1 minute and remove any wilted outer leaves. Using a sharp knife, cut out the bitter stalk in a cone shape. Place the chicory heads side by side in a shallow pot and add water until the pot is almost halfway full. Lightly salt the water, spread half the butter over the chicory, cover the pot, and simmer over low heat for approximately 20 minutes until very soft.
Remove the lid and increase the heat to medium-high. Let the cooking liquid evaporate completely, then add the remaining butter. Brown the chicory heads on all sides over medium-high heat.