Preheat the oven to 350 degrees F and line baking sheets with parchment paper.
Cream the butter and powdered sugar together in a large mixing bowl until smooth.
Stir in the egg yolk, vanilla, and rum extract until combined.
Sift in the flour and cornstarch.
Add the lemon zest and salt.
Mix until a soft dough forms.
Use a 1.5-tablespoon scoop to portion the dough.
Roll into smooth balls, place on the prepared baking sheets, and flatten with the bottom of a glass or bowl dipped in flour.
Bake until just barely beginning to turn golden on the bottoms (approx. 8 to 12 minutes).
Cool on the baking sheet.
Place about 1 teaspoon of dulce de leche on the bottoms of half the cookies, then sandwich another cookie on top.