Preparation

• Position a rack in the center of the oven and heat the oven to 400°F. Grease the bottom and sides of a 10×15-inch (4 quart) baking dish with 1 Tbs. of the butter.
• Heat the oil in a 12-inch skillet over medium heat. Working in batches so as not to crowd the pan, cook the prosciutto, stirring, until crisp, 3 to 4 minutes. Drain well on paper towels.
• Put the potatoes, cream, garlic, 1-1/2 tsp. salt, and 1/2 tsp. pepper in an 8-quart pot. Bring to a simmer over medium heat and cook, stirring occasionally, until the potatoes are barely tender when pierced with a fork, about 8 minutes.
• Meanwhile, melt the remaining 2 Tbs. butter in a heavy-duty 12-inch skillet over medium heat. Add the fennel seeds and stir just until fragrant, about 30 seconds. Add the leeks and fennel, season lightly with salt and pepper, and cook, stirring occasionally, until just tender, 8 to 10 minutes.
• Gently mix the leeks and fennel with the potatoes and the chestnuts. Transfer to the prepared baking dish, evening out the vegetables. Top with the crisp prosciutto and finish with the cheese. Bake until the cheese is deep golden brown, the cream has thickened, and the potatoes are tender when pierced with a knife, 35 to 40 minutes. (If the top is becoming too brown before the vegetables are done, cover the gratin loosely with foil.) Let cool for 10 to 20 minutes before serving.