Roast the sweet potatoes according to the recipe notes. Allow them to cool, then remove the skins and mash the flesh.
Preheat the oven to 350°F. Lightly grease a 9×13-inch baking dish.
Measure 4½ cups of mashed sweet potatoes into a large mixing bowl. Add the brown sugar, melted butter, and vanilla extract. Mix until smooth and well combined.
Taste the sweet potato mixture and add salt as needed. Once seasoned to your liking, mix in the eggs until fully incorporated.
Spread the sweet potato filling evenly in the prepared baking dish.
In a separate bowl, combine the chopped pecans, brown sugar, flour, melted butter, and cinnamon. Stir until evenly mixed, then sprinkle the pecan topping across the sweet potato filling.
Bake for 30 to 40 minutes, or until the filling is set around the edges and the pecan topping is lightly browned.
Remove the casserole from the oven and increase the oven temperature to 450°F.
While the oven heats, combine the mini marshmallows, brown sugar, and egg white in a bowl. Toss until the marshmallows are evenly coated.
Once the oven reaches 450°F, spread the marshmallow mixture evenly over the pecan topping.
Return the casserole to the oven and bake for 5 to 8 minutes. Begin watching closely after 4 to 5 minutes because the marshmallows will brown quickly.
Remove the casserole once the marshmallows are melted and golden brown. Allow it to cool slightly before serving.