Preheat your oven to 375°F and generously butter the interior of a 13x9-inch baking dish. Grab your mandoline and thinly slice the potatoes, then dice the onion and fennel bulbs with precision. Combine these vegetables in a bowl.
In a small saucepan over medium heat, melt together butter and olive oil. Add the veggies to the pan and cook until softened, about 8 minutes. Meanwhile, in another bowl mix together 2 cups of rich cream, salt, pepper, and a generous sprinkling of Gruyère cheese.
Spread half of the potato slices in an even layer on the bottom of your prepared baking dish, followed by half of the cooked vegetables and a layer of your cheese-cream mixture.
Layer the remaining potatoes, veggies, and cream mixture in that order, ending with another layer of potatoes on top. Pour the last 2 tablespoons of heavy cream over the top and finish off with a generous sprinkle of fresh salt and pepper. Bake for 1 hour or until the potatoes are tender when pierced with a fork.