Position racks in the top and bottom thirds of the oven and preheat the oven to 180C. Line two large baking sheets with parchment paper.
In a medium bowl, whisk together the cornstarch (cornflour), plain flour, baking powder, salt, and baking soda.
In a large bowl, with a hand mixer, beat the butter and white caster sugar on medium speed until pale and fluffy, 2-3 minutes. Add the egg yolks and beat until smooth. Beat in the brandy, lemon zest, and vanilla.
Add the dry ingredients and stir until the dough forms and there are no dry patches of flour remaining.
Transfer the dough to a lightly floured work surface. Using a lightly floured rolling pin, roll out the dough to 6mm thick. Using a 5cm round cutter, cut out rounds of dough and transfer them to the prepared baking sheets, spaced 2.5cm apart. Reroll the scraps to cut out more rounds.
Bake until the cookies are light golden brown at the edges and dry to the touch, 12-15 minutes, switching racks and rotating the baking sheets front to back halfway through.
Transfer the baking sheets to wire racks. Let the cookies cool on the pans for 1 minute, then transfer them to the racks to cool completely.
Flip over half of the baked cookies and top each with 1 tablespoon dulce de leche. Cover the dulce de leche with another cookie to create sandwiches.
Dust the cookie sandwiches with icing sugar, if you like, before serving.
