Preheat the oven to 400° F. Lay the halved endive in a baking pan.
Cut the stalks from the fennel bulb and discard (or keep for another use). Cut the bulb in half lengthwise, and cut very thin wedges, lengthwise, keeping part of the bulb root that holds each wedge together. If that’s not possible, don’t sweat it. The most important thing here is to cut the fennel as thinly as possible. Scatter the wedges around the endive.
Melt the butter over medium heat in a small skillet. Remove from the heat and immediately whisk in the flour to form a paste. Slowly whisk in 1/2 cup of the vegetable broth until smooth. Add half of the cheese, and the rest of the broth and pour over the endive and fennel. Add enough vegetable broth to just submerge the fennel.
Sprinkle a little salt and pepper over the top, followed by the cranberries and breadcrumbs. Just before putting the dish in the oven, sprinkle the remaining cheese on top. Cover with foil and bake for 30 minutes. Remove the foil and continue baking for another 15 minutes or until the fennel is tender and the cheese is nicely browned.