01 - In a small saucepan over low heat, melt the butter with the whole milk. Add the sugar and vanilla seeds scraped from the bean, stirring until the sugar is completely dissolved.
02 - Remove from heat and let the mixture cool slightly until lukewarm, then transfer to a large mixing bowl.
03 - Add the flour, baking powder, and salt to the wet mixture. Stir until a smooth, homogeneous dough forms.
04 - Shape the dough into a ball, wrap tightly in plastic wrap, and refrigerate for 1 hour to firm up.
05 - Preheat the oven to 350°F (conventional bake setting).
06 - On a lightly floured work surface, roll the chilled dough out to an even thickness of about ⅛ inch (3–4 mm).
07 - Using a traditional fluted rectangular cookie cutter, cut out the petit beurre shapes from the rolled dough.
08 - Place the cut biscuits onto a baking sheet lined with parchment paper, leaving a small gap between each.
09 - Gently prick each biscuit with a fork to create the classic dotted pattern. Bake for 12 minutes until golden brown.
10 - Transfer the biscuits to a wire cooling rack and let them cool completely before serving.