Preheat the oven to 400°. On a baking sheet, bake the sweet potatoes until soft, about 1 hour. Remove from the oven and lower the heat to 300°. Let the potatoes cool slightly, then peel. Transfer to a large bowl and mash.
In another large bowl, whisk together the eggs, milk, salt, nutmeg and pepper, then whisk into the sweet potatoes.
Using a food processor and working in batches, puree the sweet potato mixture. Pour into a greased 4-quart casserole dish, place on the baking sheet and bake until just set but still jiggly in the center, about 50 minutes. Drizzle with the maple syrup. Serve warm or at room temperature.