Preheat oven to 400°F. Butter 13x9x2-inch glass baking dish. Melt 1/4 cup butter in heavy large skillet over medium heat. Add leeks; sprinkle with coarse salt and pepper and cook until tender, stirring occasionally, about 12 minutes. Set aside.

Cover bottom of baking dish with 1/3 of potato slices, overlapping as needed. Layer 1/3 of ham over. Scatter 1/3 of leeks over, then 1/3 of artichoke hearts. Measure 3/4 cup cheese; set aside. Sprinkle half of remaining cheese over. Repeat layering 1 time with potato slices, ham, leeks, artichokes, and cheese. Cover with remaining potato slices, ham, leeks, and artichoke hearts.

Whisk broth and next 4 ingredients in small saucepan over medium heat until flour dissolves. Bring mixture to boil; cook until smooth and thickened, stirring often, about 3 minutes. Pour over gratin. Sprinkle 3/4 cup cheese over. Cover gratin with foil, tenting in center to prevent cheese from sticking. Bake gratin 45 minutes. Uncover and bake until potatoes are soft, topping is browned, and juices are bubbling, about 50 minutes. Let rest 15 minutes before serving.