Line a baking sheet with parchment and set aside.
In a large bowl, combine the desiccated coconut, sweetened condensed milk, vanilla extract, and salt. Stir with a spatula until the mixture is thick, sticky, and evenly moistened with no dry pockets of coconut.
Using a small cookie scoop or measuring spoon, portion the mixture into about 36 mounds, 1 tablespoon each.
Roll each mound between clean hands into a smooth 1-inch ball. If the mixture sticks too much, lightly oil or dampen your palms.
If desired, roll the balls in the extra coconut to coat, then place them on the prepared baking sheet in a single layer.
Refrigerate until firm, at least 30 minutes or up to overnight.
Serve chilled or at cool room temperature.