Preheat your oven to 425°F (220°C) and line a baking sheet with parchment paper if desired.
In a mixing bowl, whisk together the flour, baking powder, salt, and sugar until well combined.
Add the cold, cubed butter to the dry ingredients. Using a pastry cutter or your fingertips, work the butter into the flour until the mixture resembles coarse crumbs.
Gently fold in the sourdough starter and milk. Mix until just combined; be careful not to overwork the dough.
Turn the dough out onto a lightly floured surface. Pat it into a rectangle about 1-inch thick.
Using a sharp knife or biscuit cutter, cut the dough into rounds or squares, and place them on the prepared baking sheet.
Gently gather any scraps, reshape, and cut additional biscuits until all the dough is used.
Bake in the preheated oven for 18-20 minutes, until golden brown on top.
Allow the biscuits to cool slightly on the baking sheet before transferring them to a wire rack to cool completely.