Preheat oven to 375 degrees. Generously butter a 2 1/2-quart baking dish. Bring cream, broth, morels, and green garlic to a simmer.
Assemble the gratin: Peel potatoes, and cut crosswise into slices slightly thicker than 1/8 inch. Layer potatoes in dish, overlapping slightly. Spread half the leeks over top, and season with salt. Pour half the cream mixture over top. Repeat.
Cover gratin with foil, and bake 40 minutes. Uncover, and bake until potatoes are tender and golden and most of the liquid is absorbed, 20 to 25 minutes more. Let cool 15 minutes. Before serving, sprinkle with lemon zest.