Set out the buttermilk to come to room temperature. Heat the oven to 450 degrees with a rack in the center position.
Place the butter in an 8-by-8-inch baking pan (preferably oven-safe glass or ceramic) then transfer to the oven to melt, about 6 minutes. Keep a close eye on it so the butter doesn't burn. Remove from the oven and set aside.
In a medium bowl, whisk together the flour, baking powder, sugar and salt. Using a rubber spatula, stir in the room-temperature buttermilk until just combined, with no visible streaks of flour. Do not overmix.
Transfer the batter to the baking pan with butter and spread evenly with a spatula. The butter will rise to the top. Using a sharp knife, cut the batter into 9 equal-size squares. (You won’t get perfect cuts as the batter closes up.) Go over the cuts a couple of times, wiping your knife in between each cut.
Bake until the edges start to crisp and the top is golden brown, about 25 minutes, rotating the pan halfway through. Allow the biscuits to cool for about 3 minutes; they will soak up the butter bubbling in the bottom of the dish. Run a knife along the sides and through the cuts, then serve. If not serving some or all the biscuits right away, refrigerate them for up to 3 days, and reheat in a 250-degree oven until warm.