In a small saucepan, combine the broth, cream, garlic, and bay leaf; bring just to a boil. Take it from the heat and let the flavors infuse as you assemble the gratin.
Heat the oven to 350°F. Spread about one-third of the potatoes in the bottom of a 2-qt. gratin or heavy baking dish. Season with salt, pepper, and nutmeg. Next, spread about half of the leeks and half of the ham on the potatoes. Top with another one-third of the potatoes, season with salt, pepper, and nutmeg again, and top with the rest of the leeks and ham. Arrange the remaining potatoes on top, and season.
Put the gratin dish on a baking sheet (to catch any spills). Pour the cream mixture over the potatoes, discarding the garlic. Tuck the bay leaf in the center of the gratin for decoration (but don't let anyone eat it), or discard it, too. Sprinkle with the cheese.
Cover the dish loosely with foil and bake in the hot oven until the potatoes start to get tender, about 30 minutes. Remove the foil and continue baking, basting occasionally with the liquid in the dish, until the potatoes and leeks are very tender when pierced with a knife and a golden crust forms on top, another 30 to 45 minutes. Let cool for about 15 minutes before serving.