Preheat oven to 400°. Arrange one-third of potato slices in the bottom of an 8-inch baking dish or a 2-quart casserole coated with cooking spray. Top the potatoes with 1/3 cup tomato slices, 1/3 cup onion slices, 1 tablespoon basil, 1/4 teaspoon salt, and 1/4 teaspoon pepper. Repeat the layers except for salt and pepper, and sprinkle sliced ripe olives over the top layer.
Combine broth and oil, and drizzle over the potatoes. Cover with foil and bake at 400° for 40 minutes. Uncover, and bake 25 minutes or until potatoes are tender. Sprinkle potatoes with Asiago cheese, and bake for 3 minutes or until cheese melts.
Note: This recipe can also be prepared in 4 individual gratin dishes. The baking times will be the same.