To prepare cookie dough, sift the flour and salt in a large bowl. Mix in coconut. Set aside.
Cream butter and powdered sugar in a bowl of a standing mixer until light and fluffy. Beat in vanilla.
Reduce the speed to low and beat in the flour mixture until just incorporated.
Gather dough and form a dish. Cover with plastic wrap and refrigerate for about 30 minutes to chill.
Preheat oven to 350F. Line 2 baking trays with parchment paper.
On a lightly floured surface, roll out the dough to 1/4 inch thickness. Cut into 2-inch rounds using a floured cookie cutter. Place on the prepared baking sheets and place in the refrigerator for about 15 minutes.
Bake the cookies for 10 to 12 minutes, or until cookies are lightly browned.
Remove from oven and let the cookies cool a few minutes on the baking sheet before transferring them to a wire rack to cool completely.
To prepare ice cream, combine coconut milk, heavy cream, half portion of sugar and shredded coconut in a medium sauce pan. Bring mixture to simmer, until sugar is dissolved. Remove from heat.
Whisk egg yolks and remaining sugar in a medium bowl until pale, about 2 minutes. Gradually whisk in half of the warm cream mixture, mix until blended. Stir yolk mixture into the remaining cream mixture. Cook over medium heat, stirring constantly, until thick enough to coat a wooden spoon, about 2 to 3 minutes.
Strain custard into another medium bowl, let cool over a bowl of iced water or chill in the refrigerator, stirring occasionally.
Process custard in an ice cream maker according to manufacturer’s instructions. Transfer to an airtight container, cover and freeze until firm, at least 4 hours.
To assemble the sandwiches, remove ice cream from the freezer. Let sit in room temperature for easy scooping. Scoop ice cream on top of one cookie, place another cookie on top of the ice cream. Lightly press to adhere the sandwich.
Roll or sprinkle the sides with the sweetened shredded coconut.
Serve immediately. Or wrap each sandwich with plastic wrap and place them in the freezer.