Heat oven to 350°F. Coat 2 large baking sheets with nonstick cooking spray.
In medium-size bowl, beat butter, brown sugar, egg yolks, rum extract and salt on medium speed until creamy and smooth, about 2 minutes. On low speed, gradually beat in flour just until blended and soft dough forms.
Spread coconut onto a plate. Drop 1 level tablespoon dough at a time onto plate; roll to evenly coat with coconut, forming balls. Place 1 inch apart onto prepared baking sheets.
Bake in 350°F oven 18 minutes or until coconut is golden. Transfer cookies to wire rack; let cool completely.