Put the sweet potato cubes in a large pot, cover with cold water by about an inch and add a big pinch of salt. Bring to a boil, then simmer for 15 to 20 minutes, until very tender.
Drain well and return the cubes to the hot pot for 1 minute to steam off extra water.
Heat the oven to 350°F and butter a 9x13-inch (3-quart) baking dish.
Mash the sweet potatoes until smooth. Cool for about 10 minutes, then mix in 1/3 cup brown sugar, the milk, eggs, 4 tablespoons melted butter, vanilla, cinnamon and 1/2 teaspoon salt.
Spread the filling evenly in the baking dish.
Stir together the pecans, 3/4 cup brown sugar, flour, 4 tablespoons melted butter and a pinch of salt until crumbly. Scatter over the filling.
Bake for 30 to 35 minutes, until the topping is deep golden and the center is set (160°F). Rest for 10 minutes before serving.