Preheat oven to 325 degrees with racks in upper and lower thirds. Put whole and ground flaxseed, flour, baking powder, salt, and butter in the bowl of an electric mixer fitted with the paddle attachment; mix on medium speed until mixture resembles coarse meal, about 2 minutes. Stir in onion and parsley. With mixer on low speed, pour in milk. Mix until dough just comes together (do not over-mix).
Divide dough in half. Roll out each piece on a lightly floured surface to a 9-inch square (1/8 inch thick). Transfer to two baking sheets. Cut each square with a fluted pastry wheel or a knife into about 30 crackers (each 1 1/2 inches square).
Brush with egg white; season with pepper, and salt, if desired. Bake until slightly firm, about 20 minutes. Switch positions of sheets; flip crackers. Bake until light brown and firm, 18 to 20 minutes more. Transfer to wire racks to cool.