Set an oven rack to the upper-middle position and place a rimmed baking sheet on the rack. Heat the oven to 450°F. While the oven heats, place the 6 tablespoons of butter in the freezer for 10 minutes to firm up, then melt the 3 tablespoons finishing butter and set aside.
In a large bowl, whisk together the flour, baking powder, baking soda, salt, and black pepper until uniform.
Grate the chilled butter on the large holes of a box grater. Toss the shreds into the flour mixture, coating them well and lightly rubbing with fingertips until the butter is evenly dispersed but still distinct and pebbly.
In a separate bowl or large measuring cup, whisk the buttermilk, sourdough discard, and honey until smooth. Let stand for 5 minutes to hydrate and mellow the acidity.
Pour the sourdough-buttermilk mixture into the dry ingredients. Fold gently with a spatula just until no dry pockets remain. If the dough looks overly stiff, splash in 1 tablespoon more buttermilk; if too loose, sprinkle 1 to 2 tablespoons flour. Let the dough rest for 5 minutes to fully hydrate.
Carefully remove the hot baking sheet from the oven and immediately add 1 tablespoon of the melted finishing butter, tilting the pan to coat the surface (no parchment needed).
Using a heaping 1/4-cup scoop or two spoons, drop 10 to 12 mounds of dough onto the hot buttered sheet, spacing them about 2 inches apart.
Bake for 8 minutes. Open the oven briefly to brush the tops with 1 tablespoon of the remaining melted butter, rotate the pan, and continue baking 6 to 8 minutes more, until the biscuits are richly golden on the peaks and set in the centers.
Transfer biscuits to a wire rack and brush with the last tablespoon of melted butter. Cool 5 minutes before serving.