Heat oven to 350°F; line sheets with parchment.
Whisk flour, baking powder, and salt in medium bowl; set aside.
Beat butter and sugar in large bowl 3-4 minutes until fluffy.
Beat in eggs individually, mixing well after each; add lime zest, juice, and coconut extract.
Gradually mix in flour just until combined; fold in shredded coconut.
Roll into 1-inch balls; place 2 inches apart on sheets.
Bake 12-14 minutes until edges lightly golden. Cool on sheet 5 minutes; transfer to rack.
Whisk powdered sugar and lime juice into smooth, pourable glaze.
Drizzle over cooled cookies; immediately add toasted coconut.
Set glaze 15 minutes before serving or packing.