Line a baking sheet with parchment paper or a nonstick baking mat (such as Silpat).
In a large bowl, sift together flour and confectioners' sugar. In a food processor, pulse together flour, sugar, and butter until the mixture resembles coarse meal, about 20 seconds. With machine running, pour in the water in a slow stream, and process just until the dough comes together, about 20 seconds. Form the dough into two flattened disks and wrap well in plastic. Refrigerate for 1 hour.
Preheat oven to 350 degrees. On a well-floured work surface, roll out one disk of dough to a scant 1/2-inch thickness. Using a 1 1/4-inch round cookie cutter, cut out rounds from the dough and transfer to the prepared baking sheet. Repeat with the other disk of dough. Gather up scraps from both batches, and reroll and cut. Sprinkle half the rounds with sanding sugar. Bake until golden brown, about 15 minutes, rotating sheets halfway through. Transfer to a wire rack to cool completely.
About 30 minutes before serving, spread 1 teaspoon of the cold dulce de leche on the bottom of the unsugared cookies. Place the sugared cookies on top to make sandwiches. Serve immediately. Unfilled cookies can stored in an airtight container up to 3 days.
For Dulce de Leche: Empty milk into the top of a double boiler or a heatproof bowl over a pan of simmering water. Cover with a tight-fitting lid. Cook, stirring every 10 to 15 minutes, until the milk is thick and amber in color, about 5 hours. Remove from heat, and beat with a wooden spoon to smooth out. Transfer to a clean bowl, and refrigerate several hours or up to 3 days. Makes 1 3/4 cups.