Preheat the oven to 300 degrees F (150 degrees C).
Beat white sugar and butter together in a large bowl using an electric mixer until creamy. Add cornstarch, flour, eggs, pisco, vanilla extract, and baking powder. Mix gently until combined.
Turn dough out onto a clean work surface and knead by hand until smooth. Add water as needed. Divide in half, refrigerate 1 portion, and leave the other out.
Coat your work surface with powdered sugar. Roll dough out to 1/4-inch thickness and cut into 2-inch rounds with a cookie cutter or shot glass. Place rounds close together on a baking sheet. Prick each cookie twice with a fork.
Bake in the preheated oven for 10 minutes; cookies should still be white and soft, not crispy, and will firm up as they cool. Repeat with remaining cookie dough.
Pour condensed milk, evaporated milk, and brown sugar into a saucepan over medium-low heat. Stir constantly until filling approaches the consistency of thick caramel, 20 to 30 minutes. Remove from heat; mixture will firm up as it cools to room temperature, about 30 minutes.
Pour confectioners' sugar into a shallow bowl. Spread about 1/2 tablespoon of the filling over cooled cookies. Attach every two cookies together to make the alfajores. Roll alfajores in confectioners' sugar.