Heat oven to 325° F.
Line two baking sheets with parchment paper.
Add the coconut, sweetened condensed milk, and vanilla to a mixing bowl. Mix thoroughly.
In a separate mixing bowl, use a hand mixer to beat together the egg whites and salt until soft peaks form that hold their shape.
Gently fold the egg whites into the coconut mixture.
Use a small cookie scoop to form 1-inch to 1 1/2-inch balls and place on the prepared cookie sheet about 1-inch apart. You should get about 24 cookies, or about 20 if using the larger scoop.
Bake for 20 to 25 minutes, or until the tops of the cookies turn a light golden brown, and the bottoms are golden brown.
Cool and then serve.
Store in an air-tight container.