Heat the oven to 350 degrees Fahrenheit.
Using butter, grease the casserole dish.
Make a lengthwise cut in the bulbs of the fennel and remove the stalks.
Cut the bulbs crosswise and remove the cores (hearts). Fennel slices should make approximately 3 or 4 cups.
Using olive oil and butter, fry the fennel and onions on low heat for 15 minutes, until tender. If you would like, you can add some minced garlic at this point.
By hand or with a mandolin, peel and thinly slice the potatoes.
With salt, black pepper, and 2 cups of cream, combine the sliced potatoes with the Gruyère cheese, 2 cups of cream, and 2 cups of cheese.
Mix the onion and fennel together.
In a baking dish, place the potato mixture.
Create an even layer by pressing the mixture.
Sprinkle the potatoes with the remaining 2 tablespoons of cream and ½ cup of Gruyère cheese. If you like, you can add some pepper to the mixture as well.
In a large baking dish, bake the potatoes for 1 ½ hours until very tender and lightly browned on top.
Before serving, let the potatoes cool for 10 minutes.