Step 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.

Step 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.

Step 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.