Cook the sweet potatoes. Place the sweet potatoes in a large pot. Add enough water to cover them a little more than halfway. You will need at least 3-4 inches of water, but the potatoes should not be completely submerged. Bring the water to a boil, then reduce the heat to a medium simmer. Cover and cook until the potatoes are tender when pierced with a fork. Depending on their size, this can take 20-40 minutes. Avoid cooking them until mushy.
Peel the potatoes. Drain the water and transfer the sweet potatoes to a plate or cutting board. Let them cool until they can be handled comfortably. Remove and discard the skins, then place the peeled potatoes in a large mixing bowl.
Prepare the filling. Add the eggs, evaporated milk, vanilla, sugar, salt, and melted butter. Mash until smooth. Begin with a potato masher, then use an electric mixer on low speed for about 45 seconds to create a smooth consistency.
Transfer to the baking dish. Spoon the mixture into a lightly greased casserole dish. An 8×11-inch dish, 9×13-inch dish, or deep-dish 10-inch pie pan will work.
Make the pecan topping. Put the flour, brown sugar, and chopped pecans in a mixing bowl. Add the butter and work it into the mixture with a fork or pastry blender until thoroughly combined. Distribute the topping evenly over the sweet potato mixture.
Bake. Bake at 350°F for 35-40 minutes.
Store leftovers. Keep leftover casserole refrigerated for 4-5 days.