Preheat oven to 350 degrees F (175 degrees C). Line 2 baking sheets with parchment paper.
Whisk cornstarch, flour, baking powder, and baking soda in a bowl.
Beat butter and sugar with an electric mixer in a large bowl until light and fluffy. Whisk in egg yolks, one at a time, until well combined. Add lemon zest and vanilla extract with the last egg. Fold into flour mixture with a spoon, mixing until dough holds together and turns into a ball. Wrap in plastic wrap; refrigerate for 30 minutes to 1 hour.
Roll out dough to about 1/4-inch thickness. Cut cookies with a small round cookie cutter and place on the prepared baking sheets.
Bake in the preheated oven until set but not browned, 7 to 10 minutes. Remove immediately to cool on a wire rack.
Spread underside of a cookie with 1 teaspoon dulce de leche. Sandwich together with another cookie until filling comes out on the sides. Roll sides in the shredded coconut.