Place mushrooms in a spice grinder, and grind until fine, about 15 seconds.
Preheat oven to 350 degrees. In the bowl of a mixer fitted with the paddle, mix butter and blue cheese on medium until combined. Add flour, ground mushrooms, and pepper; mix just until combined and crumbly. Add milk, and mix just until dough comes together (the dough will be quite stiff).
Divide dough evenly into three disks. Wrap two disks in plastic wrap; set aside. On a lightly floured work surface, roll out one disk to be 1/16 inch thick. Cut out crackers with a 31/2-inch round cutter. Transfer to a baking sheet; prick each with a fork three or four times. Sprinkle lightly with salt.
Repeat with remaining dough. Bake until golden brown, about 22 minutes. Let cool completely on a wire rack. Store crackers in an airtight container up to 1 week.
The dough can be frozen, wrapped in plastic, up to three months.