Preheat oven to 350° F/175° C. Toast the coconut on a rimmed baking sheet until light golden, stirring occasionally, about 10 to 12 minutes.
In the bowl of the stand mixer beat the butter, ½ cup powdered sugar, and both extracts to blend well. Beat in flour, orange peel, and salt. Stir in toasted coconut. Cover and refrigerate at least 1 hour and up to 1 day. Soften dough slightly before shaping.
Preheat oven to 350° F/175° C. Line 2 large baking sheets with parchment paper.
Using 1 level tablespoon dough for each cookie, roll dough between palms of hands into balls. Place on prepared sheets, spacing 1 inch apart. Bake until golden on bottom but pale on top, about 16 to 18 minutes. The trick is to make sure they don’t dry out, so don’t let them overcook. Transfer cookies to racks and cool 5 minutes.
Place remaining 1-¾ cups powdered sugar in a bowl. Roll hot cookies in powdered sugar, covering completely. Cool cookies on rack. Roll cookies in powdered sugar again, coating generously. (Can be made 5 days ahead. Store airtight between sheets of waxed paper at room temperature.)