Preheat oven to 375°F (190°C).

Butter a 13x9x2-inch glass baking dish.

Melt 2 tablespoons of butter in a large nonstick skillet over medium heat.

Add chopped leeks, cover, and cook until tender, stirring occasionally, for about 10 minutes.

Remove from heat.

Chop enough fennel fronds to measure 1/2 cup; set aside.

Discard any remaining fennel fronds.

Arrange half of the fennel slices in a single layer in the prepared baking dish.

Sprinkle with 1/4 cup fennel fronds, salt, and pepper.

Top with half of the sliced potatoes in a single layer.

Arrange half of the leek mixture over the potatoes.

Sprinkle generously with salt and pepper.

Sprinkle with half of the grated Parmesan cheese.

Repeat layering with remaining fennel slices, fennel fronds, potatoes, leek mixture, and Parmesan cheese.

Sprinkle the potato gratin generously with salt and pepper.

Bring chicken stock and whipping cream to a boil in a medium saucepan.

Pour the mixture over the potato gratin.

Bake uncovered until the vegetables are very tender, the liquid is almost absorbed, and the top is deep golden brown, about 1 hour 10 minutes.

(Can be prepared 2 hours ahead. Let stand at room temperature. Cover gratin with aluminum foil and rewarm in a 375°F (190°C) oven for about 20 minutes.)