Preheat oven to 375°F. Butter 13x9x2-inch glass baking dish. Melt 2 tablespoons butter in large nonstick skillet over medium heat. Add leeks; cover and cook until tender, stirring occasionally, 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 fennel slices in single layer in prepared baking dish; sprinkle with 1/4 cup fennel fronds, salt and pepper. Top with half of sliced potatoes in single layer. Arrange half of leek mixture over. Sprinkle generously with salt and pepper. Sprinkle with half of grated Parmesan cheese. Repeat layering with remaining fennel slices, fennel fronds, potatoes, leek mixture and Parmesan cheese. Sprinkle potato gratin generously with salt and pepper.
Bring chicken stock and whipping cream to boil in medium saucepan. Pour mixture over potato gratin. Bake uncovered until vegetables are very tender, liquid is almost absorbed and 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 375°F oven about 20 minutes.)