Step 1In a large bowl, using an electric mixer on medium-high speed, cream butter, brown sugar, and granulated sugar until light and fluffy. Add egg and vanilla and beat until smooth. Fold in flour, baking soda, salt, and 1 cup coconut until combined. Cover bowl and refrigerate at least 1 hour or up to overnight.
Step 2Preheat oven to 350° and line 2 large baking sheets with parchment. Place remaining 1 1/2 cups coconut in a medium bowl.
Step 3Portion dough into balls using a tablespoon measuring spoon and roll to coat in coconut. Arrange on prepared baking sheets, spacing 2" apart.
Step 4Bake until edges are golden, 11 to 13 minutes.
Step 5Let cool completely on baking sheet before serving.
Step 6Make Ahead: Cookies can be made 2 days ahead; store in an airtight container at room temperature, or freeze up to 1 month.