Peel and cube the sweet potatoes, then boil them in a large pot covered with water until tender, about 15-20 minutes. Drain and let cool slightly.
Mash the sweet potatoes in a mixing bowl, then stir in brown sugar, milk, melted butter, vanilla extract, cinnamon, nutmeg, and salt until smooth.
In a separate bowl, mix chopped pecans, flour, granulated sugar, and softened butter until crumbly.
Spread the sweet potato mixture evenly in a greased 9x13-inch baking dish and sprinkle the pecan crumble topping over it.
Preheat the oven to 350°F (175°C) and bake the casserole for 30-35 minutes until the topping is golden brown.