Divide the dough in half. Roll each portion between two sheets of parchment paper into an even rectangle about ¼ inch thick. Transfer to the freezer and chill until firm but pliable, 10 to 15 minutes.

Heat the oven to 350°F/175°C convection. Remove the parchment, cut the dough into rounds of the desired size, and arrange on parchment-lined baking sheets, leaving a small space between cookies. Bake until set but still pale, about 12 minutes; the cookies should not brown.

Let cool completely. Spoon dulce de leche onto the flat side of half the cookies, sandwich with the remaining cookies, and gently roll the edges in shredded coconut. Store airtight or serve immediately.