Preheat the oven to a moderate 350°F.
Peel and delicately mash the sweet potatoes until they reach an even, creamy consistency.
In a separate bowl, beat together the eggs and sugar until light and airy. Gradually add in the mashed sweet potatoes, milk, salt, butter and vanilla extract, ensuring all ingredients are adequately combined throughout.
Grease a baking dish generously with butter before pouring in the sweet potato mixture, spreading it evenly across the surface.
For the topping, mix together brown sugar, flour and melted butter in a bowl until they form an even combination. Sprinkle this delightful blend of ingredients overtop of the sweet potato mixture.
Bake for 40 to 45 minutes, or until the top of the dish is golden brown. Allow it to cool for 10 minutes before serving.