Preheat the oven to 425F.
In a large bowl, stir together the flour, baking powder, baking soda and salt. Slice or cut the butter into the flour mixture, or grate it on the coarse side of a grater. Toss to combine, or rub bigger pieces into the flour with your fingers—don’t rub it all the way in, you want some bigger pieces left.
In a measuring cup, stir together your sourdough starter and buttermilk, add to the dry ingredients and stir just until the dough comes together. (It will be a bit shaggy.) Gather it all up, including all the rough bits in the bottom of the bowl, and either pat it out an inch thick on a parchment-lined baking sheet or, if you like, pat it out about half an inch thick and fold it over itself in thirds, as if you were folding a letter. (This will give you satisfying layers, but it’s truly not necessary.)
Pat the dough about an inch thick and cut into wedges, squares or rounds with a sharp knife or cookie cutter. (If you’re using a cutter or glass rim, try not to twist it, as this could seal the cut sides a bit, keeping them from maximum lift.) Brush the tops with a but more buttermilk or cream (there should be enough in the bottom of the measuring cup) and bake for 15-20 minutes, or until risen and deep golden. Makes about 8 biscuits.