Preheat oven to 400 F. Lightly grease a 9 x 13 baking dish.
Trim the fennel bulbs of their stems and fronds. Then cut them in half and remove the core. (Pro tip: The fronds can be reserved for an aromatic garnish.)
Peel the potatoes. Thinly slice the fennel and potatoes to about 1/8 inch.
Pour in enough cream to coat the bottom of the baking dish. Place one layer of potatoes down, then lightly salt and pepper, and sprinkle on cheese and dot with butter.
Next do the same with a layer of fennel. Continue alternating until the fennel and potatoes have been used up, leaving the top of the vegetables cheese-free. Reserve about 1/3-1/2 cup cheese.
Pour remaining cream over top.
Bake until potatoes are tender, about 45 minutes. Sprinkle with remaining cheese, then bake until golden brown, about 15-20 minutes.