In the bowl of a stand mixer fitted with the paddle attachment, beat the cold butter, granulated sugar, and powdered sugar on medium speed until smooth and creamy. Add the flour and salt, and mix just until a soft, uniform dough forms. Wrap and refrigerate for 1 hour.

Preheat the oven to 320°F/160°C (static mode). Line an 8-inch/20 cm square baking pan with parchment paper.

Press half the chilled dough (or two-thirds for a thicker crust) evenly into the prepared pan. Smooth the surface with an offset spatula. Refrigerate the remaining dough. Bake the base for 12 minutes, until lightly golden at the edges. Cool for 10 minutes.

Warm the dulce de leche in the microwave for about 20 seconds to loosen. Spread gently over the cooled crust. Crumble the remaining dough into small pieces and scatter evenly over the dulce de leche layer.

Bake for about 30 minutes, until the top turns lightly golden. Cool completely, at least 1 hour. Lift from the pan and cut into squares.