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Preparation Preheat oven to 425°. Stir together baking powder, baking soda, kosher salt, sugar, and 1½ cups flour with a fork in a large bowl. Add ½ cup chilled butter and toss with your hands or fork just to coat. Using your fingers, smash butter into flat disks (if you miss a few, it will be fine). Using a pastry cutter or fork, work butter into dry ingredients until shaggy crumbles form (you should have some large pieces, some small pieces, some flat pieces, and some sandy flour).
Add sourdough starter and mix gently with fork to incorporate, then fold with your hands just until dough comes together with just a few crumbly pieces in the bottom of the bowl.
Transfer dough to a well-floured surface and pat out with your hands until about ½” thick (the shape doesn’t matter too much at this point). Fold into thirds as you would a letter to create a rough rectangle. Working from short sides, fold in thirds like a letter again. Pat dough out to a ½”-thick square. Repeat folding process. Pat out dough for a third time to a 1”-thick square—it should feel airy, like a pillow at this point. Using a floured 2½”-diameter biscuit cutter or glass, punch out as many biscuits as you can (do not twist cutter). Transfer biscuits to a parchment-lined rimmed baking sheet, spacing at least 1” apart.
Using your hands, gently press scraps into a rectangle, then fold in half. Pat out to a 1”-thick rectangle and cut out more biscuits. Gather remaining scraps together to form 1 final biscuit (you should have 10 total). Transfer to baking sheet. Brush biscuit tops with 2 Tbsp. melted butter and sprinkle with sea salt if desired
Bake biscuits until tall and golden and an instant-read thermometer inserted into the side of a biscuit registers 205°F), 12–15 minutes.