Place the potatoes in a large pot and add enough cold water to cover. Bring to a boil and add 2 teaspoons salt. Reduce heat and simmer until very tender, 20 to 25 minutes. Drain the potatoes and return them to the pot.
Meanwhile, heat oven to 325° F. In a small bowl, combine the coconut, brown sugar, pecans, and ½ teaspoon salt.
Add the granulated sugar, milk, butter, eggs, vanilla, and ½ teaspoon salt to the potatoes and mash until smooth.
Transfer the mixture to an 8-inch square or another shallow 2-quart baking dish and sprinkle with the coconut mixture. Bake until heated through (tent loosely with foil if the top browns too quickly), 30 to 35 minutes.