1. Preheat oven to 425°. Process first 5 ingredients in a food processor fitted with the chopping blade, 3 to 5 seconds or until garlic is finely chopped. Pulse in flour and 1/2 cup half-and-half, then pulse in remaining half-and-half. Transfer to a medium saucepan.
2. Remove chopping blade from the processor, and insert medium slicing disk. Stand chunks of baking and sweet potato side by side in feed tube, and pulse through the disk. Repeat until all potatoes are sliced. Spread half the potatoes in a lightly greased shallow 2-quart baking or gratin dish.
3. Cook cream mixture over high heat, stirring constantly, for 3 minutes or until it starts to boil. Pour half the boiling cream mixture evenly on top of potatoes; add remaining potatoes, and repeat with remaining cream mixture. Dot with butter.
Note: At this point, you can cover the dish with foil and refrigerate for several hours. Before baking, let stand for 30 minutes at room temperature, and bake, uncovered.
4. Bake at 425° on the middle oven rack for 35 minutes or until potatoes are crusty-brown on top and tender underneath. Sprinkle cheese on top, and bake 10 more minutes.