Preheat an oven to 375 degrees F (190 degrees C). Butter a shallow 3-quart (3-liter) baking dish.

In a small saucepan, combine the broth, cream, garlic and sage. Bring to a boil, then reduce the heat to low and simmer, uncovered, for 15 minutes.

Meanwhile, trim any fat from the ham steak, if using, and remove and discard the center bone. Cut the ham steak or baked ham into 1/2-inch (12-millimeter) dice. Arrange one-third of the potatoes in a layer on the bottom of the prepared dish. Top with half of the diced ham and one-third of the shredded cheese. Repeat the layers of potatoes, diced ham and shredded cheese. Top with the remaining potatoes and the remaining cheese.

Remove the broth-cream mixture from the heat. Remove and discard the garlic cloves. Season the broth-cream mixture to taste with pepper and pour over the layered vegetables, distributing it as evenly as possible. Bake, uncovered, until the potatoes are tender when pierced and the top is brown, about 1 hour. Remove from the oven and let stand for about 5 minutes before serving.