Place the sweet potatoes in a large pot and cover with salted water. Bring to a boil over high heat and cook until very tender, about 15-20 minutes.
Drain the sweet potatoes thoroughly and transfer them to a mixing bowl. Mash until smooth and creamy, with no lumps.
In a small bowl, combine brown sugar, melted butter, and vanilla extract. Mix well until the sugar dissolves slightly.
Fold the sugar mixture into the mashed sweet potatoes until evenly combined. Transfer the mixture into a buttered 9x13 inch baking dish, spreading it out smoothly.
In a separate bowl, prepare the pecan streusel by combining flour, granulated sugar, cinnamon, and cold butter. Use a fork or pastry cutter to mix until the mixture resembles coarse crumbs.
Sprinkle the chopped pecans evenly over the sweet potato layer, then top with the streusel mixture, pressing lightly to adhere.
Bake in the preheated oven at 180°C (350°F) for 25-30 minutes, until the topping is golden brown and bubbling around the edges.
Remove the casserole from the oven and let it rest for a few minutes. Serve warm, enjoying the crispy topping and creamy interior.