Preheat the oven to 400°F (200°C). Prick the sweet potatoes with a fork, place them on a baking sheet, and roast until tender, about 45–60 minutes depending on size. Alternatively, microwave on high for 8–12 minutes, turning halfway, until soft.
When the sweet potatoes are cool enough to handle, split and scoop the flesh into a large bowl. Mash until smooth with a potato masher or pass through a ricer for extra silkiness.
Add the butter, brown sugar, vanilla, milk, cinnamon, nutmeg, and salt to the mashed sweet potatoes. Stir until combined and creamy. Taste and adjust sweetness or spices as needed.
Transfer the sweet potato mixture to a buttered 9x13-inch baking dish (or equivalent). Smooth the top with a spatula to create an even layer.
Make the candied pecans: In a medium skillet over medium heat, combine the granulated sugar and water. Stir until sugar dissolves and begins to bubble. Add the pecan halves and butter, stirring to coat. Continue cooking until the sugar crystallizes slightly and coats the nuts, about 3–5 minutes. Immediately transfer the pecans to a parchment-lined tray to cool and harden.
Coarsely chop the candied pecans and scatter them evenly over the sweet potato layer. Sprinkle the mini marshmallows over the pecans in a single even layer.
Lower the oven temperature to 350°F (175°C). Bake the casserole until heated through and marshmallows begin to puff and turn golden, about 12–15 minutes. For a darker, toasted top, switch the oven to broil for 1–2 minutes — watch closely to prevent burning.
Remove the casserole from the oven and let it rest for 5 minutes. If desired, drizzle with a tablespoon of maple syrup for extra shine and flavor. Serve warm.