Cook the Sweet Potatoes: Scrub the sweet potatoes and place them in a large saucepan. Cover with water and bring to a boil. Lower the heat to medium and cover the pan. Cook for 40 to 55 minutes or until they are tender. Drain and let them stand until cool enough to handle.

Prepare the Oven and Baking Dish: Heat the oven to 375°F and butter a 2 to 2 1/2-quart casserole.

Peel the Sweet Potatoes: Slip the skins off of the sweet potatoes and place them in a large bowl with 1/2 cup of softened unsalted butter, 3/4 cup of brown sugar, and 1/2 teaspoon of salt. Combine the milk, eggs, and vanilla in a separate small bowl. Whisk until smooth.  Use an immersion blender, whisk, or electric mixer to beat the sweet potato mixture until smooth. Add the egg mixture and whisk until well blended. Spread the mixture in the prepared baking dish. 

Prepare the Topping: Combine 1/2 cup of brown sugar, 1/2 cup of flour, 1/2 cup of cold butter, and a pinch of salt in a bowl. Using your fingers, work the butter into the flour and sugar mixture to form crumbs. Work the pecans into the crumbs.

Finish the Dish: Transfer the sweet potato filling to the prepared baking dish and spread it evenly. Sprinkle the pecan mixture over the filling.

Bake: Bake the casserole in the preheated oven for 35 to 45 minutes or until the filling is set and the topping is browned.