Mix flour, baking powder, and salt together in the bowl of a stand mixer with a paddle attachment. Add unsalted butter and mix at medium speed until well incorporated and the mixture resembles wet sand, about 4 minutes.
Remove the bowl from the mixer and fold in buttermilk until dough sticks together.
Dump dough onto a flour work surface; pat into a rectangle. Pat remaining dry crumbs into the mixture by hand.
Cut dough in half with a floured bench knife; stack cut halves on top of each other. Press layers together to about 1 1/2-inch thickness, shaping a long rectangle as you go. Repeat 3 to 5 times.
Cut dough into 8 even squares with the bench knife. Cut off uneven edges and put these scraps to the side; clean cuts on all sides will encourage rise. Pat scraps together to make 1 odd-shaped ninth biscuit.
Place biscuits close together in a 9-inch square pan and brush with melted salted butter. Place pan on top of the warm stove for 10 to 15 minutes to rise.
Bake biscuits in the preheated oven, checking halfway through bake time, until tops are golden brown and a toothpick inserted into the center comes out clean, 14 to 18 minutes.