Preheat oven to 400°.
Pulse baking powder, salt, sugar, baking soda, and 3½ cups flour in a food processor to combine.
Add chilled butter and pulse until largest pieces of butter are the size of a pea.
Transfer to a large bowl and gradually drizzle buttermilk over top, tossing with a fork as you go to incorporate. Lightly knead the mixture a few times in bowl until a shaggy dough forms (mixture will look a little dry), then turn out onto a clean surface and divide the dough into two balls.
Pat each ball into a 1 inch thick square. Stack the squares on top of each other, sandwiching any loose dry bits of dough between the two layers, and press down to flatten.
Lift up the dough with a bench scraper and dust the surface with flour. Roll dough into a 1 inch thick rectangle. Cut into a 4x3 grid to make 12 biscuits. Transfer to a parchment-lined baking sheet, spacing 2 inches apart. Freeze the shaped biscuits for 10 minutes.
Remove from the freezer and brush the tops of biscuits with melted butter. Bake the biscuits until golden on top, about 20–25 minutes.
Best served fresh with a liberal spreading of butter and a drizzle of honey.