01 - In a small saucepan over low heat, gently melt the butter with the whole milk. Add the granulated sugar and vanilla seeds scraped from the bean, stirring continuously until the sugar has fully dissolved and the mixture is smooth.
02 - Remove the saucepan from heat and allow the butter-sugar mixture to cool slightly until lukewarm, then transfer it to a large mixing bowl.
03 - Add the all-purpose flour, baking powder, and fine sea salt to the bowl. Stir with a wooden spoon or spatula until a homogeneous, smooth dough forms and no dry pockets of flour remain.
04 - Shape the dough into a ball, wrap it tightly in plastic wrap, and refrigerate for at least 1 hour to firm up and make it easier to roll out.
05 - Preheat your oven to 350°F (180°C) using conventional bake setting. Line a baking sheet with parchment paper and set aside.
06 - On a lightly floured work surface, roll the chilled dough out to an even thickness of about ⅛ inch (3–4 mm), rotating it occasionally to prevent sticking.
07 - Using a traditional fluted rectangular cookie cutter, cut out the petit beurre shapes from the rolled dough. Gather and re-roll any scraps to cut additional biscuits.
08 - 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 air bubbles.
09 - Bake on the center rack for 12 minutes, or until the edges are lightly golden and the tops have taken on a warm blonde color. Rotate the sheet halfway through for even browning.
10 - Transfer the biscuits to a wire cooling rack and let them cool completely before serving. This allows them to crisp up and develop their signature snap.