Preheat the oven to 425°F, with a rack in the upper third.
Grease a baking sheet, or line it with parchment.
Combine the flour, baking powder, and salt.
Work the butter into the flour until the mixture is unevenly crumbly.
Add the starter, mixing gently until the dough is cohesive.
Turn the dough out onto a lightly floured surface (a piece of parchment works well), and gently pat it into a 6-inch round about 1-inch thick.
Use a sharp 2 ⅜-inch biscuit cutter to cut four rounds, cutting them as close to one another as possible.
Gently push and pat the scraps into a 2 ½-inch x 5-inch rectangle. Cut two more biscuits.
Push and pat the remaining scraps into a 1-inch thick biscuit; it will be slightly smaller than the others.
Place the sourdough biscuits onto the prepared baking sheet, leaving about 2 inches between them; they will spread as they bake.
Bake the sourdough biscuits in the upper third of your oven for 20 to 23 minutes, until they are golden brown.
Remove the sourdough biscuits from the oven, and serve warm or cool completely, wrap in plastic, and store at room temperature for several days. Freeze, well-wrapped, for longer storage.
