In a mixing bowl, combine 2 cups (250g) all-purpose flour, 1 cup (100g) sugar, 1 tablespoon (14g) baking powder, and ½ teaspoon (3g) salt.
Grate 8 tablespoons (113g) butter on a large hole grater.
Add shredded butter to flour mixture and lightly mix with fingers until combined and butter pieces are completely coated in flour.
In a liquid measuring cut, mix together ¾ cup (173g) buttermilk and ¾ teaspoon vanilla bean paste.
Form a well in center of flour mixture; pour buttermilk-vanilla mixture into well and using a rubber spatula, mix gently until a shaggy dough comes together.
Transfer dough to a work surface and lightly press dough into a rough 8✕5-inch rectangle (about 1-inch thick)
Fold rectangle into thirds (like a letter) and press down into a 1-inch thick rectangle. Repeat folding and pressing twice more. Chill for 5 minutes if dough gets really soft or sticky.
Shape rectangle into a rough 8✕5-inch rectangle (about 1¼-inches thick). Transfer to a parchment-lined baking sheet and chill in fridge 30 minutes.
Meanwhile, heat oven to 425ºF (218ºC) with rack set in middle position.
Melt remaining 2 tablespoons butter in a heatproof bowl in the microwave.
Cut biscuit dough in half lengthwise then cut each half into 4 squares; arrange on parchment-lined baking sheet.
Brush biscuits with melted butter then sprinkle with sugar to coat.
Bake until risen and golden brown on tops and sides, 20–21 minutes, rotating halfway through. Let cool on sheet 5 minutes, then transfer to a cooling rack to cool completely.