Preheat the oven to 350 degrees F.

Butter the inside of a 10-by-15-by-2-inch (10-cup) baking dish.

Remove the stalks from the fennel and cut the bulbs in half lengthwise. Remove the cores and thinly slice the bulbs crosswise, making approximately 4 cups of sliced fennel. Saute the fennel and onions in the olive oil and butter on medium-low heat for 15 minutes, until tender.

Peel the potatoes, then thinly slice them by hand or with a mandoline. Mix the sliced potatoes in a large bowl with 2 cups of cream, 2 cups of Gruyère, salt, and pepper. Add the sauteed fennel and onion and mix well.

Pour the potatoes into the baking dish. Press down to smooth the potatoes. Combine the remaining 2 tablespoons of cream and 1/2 cup of Gruyère and sprinkle on the top. Bake for 1 1/2 hours, until the potatoes are very tender and the top is browned and bubbly. Allow to set for 10 minutes and serve.