In the bowl of a food processor fitted with the steel blade, combine the flour, salt, confectioners' sugar, pecans and coconut. Process until the pecans and coconut are finely ground, and the mixture looks like sand. Add the butter, lime zest, and vanilla extract; process until the mixture comes together into a cohesive dough. Remove the dough from the bowl and wrap in plastic. Chill until firm enough to roll, 45 minutes to 1 hour.

Meanwhile, preheat the oven to 350°F. Line two baking sheets with parchment paper.

Measure the dough into heaping teaspoon-size pieces and roll each piece into a ball. Place the balls about 1-1/2 inches apart on the prepared baking sheets. Bake until the edges of the cookies barely begin to brown, 12 to 14 minutes. Let cool on the baking sheets, then roll in the confectioners' sugar while still warm. Let the cookies cool on a rack, then roll again in confectioners' sugar once they are cool. Store in an airtight container at room temperature.