For filling, scrape condensed milk into a heavy-bottomed saucepot. Heat over medium heat and bring to a simmer, stirring constantly. Continue to cook milk until it thickens and becomes a rich caramel colour, stirring constantly (I switch between a whisk and heatproof spatula). This takes about 20 minutes. Remove from heat and scrape dulce de leche into a heatproof bowl (glass or plastic might melt initially), stir in vanilla and allow to cool to room temperature.
For layers, preheat oven to 350 °F. Combine flour, sugar, baking powder and salt. Cut in butter until dough is an even crumbly texture. Add milk and combine until dough comes together. Shape dough into a disc, wrap and set aside to rest for 20 minutes.
On a lightly floured surface, roll out pastry to ¼-inch thick and cut out 24 discs 1 ½ -inches across. Line discs on a parchment-lined baking sheet and dock with a fork. Bake for about 6 minutes, until they brown just slightly on the bottom, but take no colour on top. Allow to cool.
To assemble, spread a generous spoonful of dulce de leche on a cookie and top with another, pressing gently. Repeat with more filling and cookies, so that each has four cookies filled. Top with a generous dusting of icing sugar and chill until ready to serve.
These tortes are great made at least a day ahead and refrigerated, to soften. They can also be frozen.