1. Heat oven to 350 degrees. Heat olive oil in a small pot over medium heat. Add flour and cook, stirring, 1 minute. Slowly whisk in milk and 1 cup water. Cook, whisking, until thick enough to coat the back of a spoon, about 12 minutes. Remove from heat and stir in 1/4 cup Parmesan and the chopped sage. Season with salt and pepper.

2. Pour a third of the sauce in the bottom of a 9-by-13-inch casserole dish. Arrange a third of the sweet potato and cauliflower slices along the bottom. Season with salt and pepper. Repeat twice with remaining sauce and vegetables. Cover dish with parchment-lined foil and bake until vegetables are tender, about 1 hour. Raise oven temperature to 425 degrees. Remove foil and sprinkle with remaining tablespoon of cheese. Bake until golden brown, about 20 minutes. Let stand 10 minutes before serving.

3. Meanwhile, crisp sage leaves: Heat 1 inch vegetable oil in a small pot over medium-high heat until surface is shimmering slightly. Add a few leaves at a time (they'll bubble up) and cook until crisp, but still bright green, about 10 seconds. Transfer to a paper towel to drain. Season with salt. Top gratin with leaves.