Preheat the oven to 220°C (425°F).
In a large bowl, whisk together the whole wheat flour, all-purpose flour, baking powder, baking soda, and salt.
Add the cold cubed butter. Using a pastry cutter or two knives, cut the butter into the flour until the largest pieces are about the size of peas.
Stir in the cold sourdough discard and cold milk just until a shaggy dough forms and no large dry pockets of flour remain.
Turn the dough onto an unfloured work surface and gently press it together. Fold it over itself two or three times to create layers, handling it as little as possible.
Lightly flour the surface and gently pat or roll the dough to 1 inch thick.
Cut the biscuits with a sharp biscuit cutter, pressing straight down without twisting. Arrange them on an ungreased baking sheet so the sides are just touching.
Gather the scraps gently and cut additional biscuits.
Bake for 10–12 minutes, until well risen and golden brown. Brush with melted butter, if desired, and serve warm.