WHISK flour, cornstarch, baking powder and salt in a medium bowl.
BEAT butter and sugar in a large bowl with an electric mixer on medium until fluffy, about 3 min. Add egg yolk, brandy and vanilla and beat until combined, 30 sec. Beat in flour mixture on low until just combined.
DIVIDE in half and wrap in plastic wrap. Flatten into discs and refrigerate until firm, 1 ½ hr.
PREHEAT oven to 350F. Line a baking sheet with parchment.
ROLL dough on a large piece of parchment to ¼-in. thickness. Refrigerate on another baking sheet for 20 min. Cut out shapes using a 1 ½-in. round cookie cutter, rerolling scraps and refrigerating as needed. Place cookies ½ in. apart on prepared sheet.
BAKE until cookies are firm and bottoms are light golden, 11 to 12 min. Cool for 2 min, then transfer to a rack to cool. Repeat with remaining dough.
FLIP half of the cookies over and spread 2 tsp dulce de leche on each. Gently sandwich with remaining cookies. Roll sides of cookies in coconut to coat, then dust with icing sugar before serving.