01 - Gently melt the butter with the whole milk in a small saucepan over low heat. Add the sugar and vanilla seeds scraped from the bean, stirring until the sugar has fully dissolved. Remove from heat and let the mixture cool until lukewarm.
02 - Transfer the lukewarm liquid mixture to a large mixing bowl. Sift in the flour, baking powder, and salt. Stir with a wooden spoon until a smooth, homogeneous dough forms.
03 - Shape the dough into a ball, wrap it tightly in plastic wrap, and refrigerate for at least 1 hour to firm up and make rolling easier.
04 - Preheat the oven to 350°F (conventional bake setting). Line a baking sheet with parchment paper.
05 - On a lightly floured work surface, roll the chilled dough out to an even thickness of about ⅛ inch (3–4 mm). Use a traditional rectangular fluted cutter to stamp out the petit beurre shapes, rerolling scraps as needed.
06 - Place the cut biscuits onto the prepared baking sheet, spacing them about ½ inch apart. Gently prick each biscuit several times with a fork to create the classic dotted pattern and prevent puffing during baking.
07 - Bake on the middle rack for 12 minutes, or until the edges turn a light golden brown. Keep a close eye on them during the last couple of minutes to avoid over-browning.
08 - Transfer the biscuits to a wire cooling rack and let them cool completely before serving. Once fully cooled, store in an airtight container at room temperature for up to two weeks.