To make the dough: Sift together the flours, dry milk, baking powder, baking soda, salt, paprika and cheese powder in a large bowl or a food processor.
Cut in the butter, using a pastry blender or the metal blade of the food processor, until the mixture is a fine meal.
Add the buttermilk and mix until the dough comes together—it'll be very moist and sticky.
Turn out the dough onto a floured board and knead lightly for a minute or two, incorporating extra flour as needed to keep the dough from sticking to the surface.
Pat the dough into two flat rounds, wrap in plastic and chill for 30 minutes.
Preheat oven to 325 degrees F.
To shape the crackers: Remove one piece of dough from the refrigerator and place it on a generously floured surface.
Using a floured rolling pin, roll the dough into a large square. You'll want to make this very thin—no more than 1⁄16 inch thick. As you roll, be sure to lift, turn and reflour frequently. The dough will be very tender and sticky, but be sure to roll it thin enough.
Trim the edges using a pizza cutter or sharp knife and cut the dough into 1-inch squares.
To bake the crackers: Place the squares close together on a baking sheet lined with parchment paper.
Use a cake tester to poke a small hole in the center of each cracker.
Bake the crackers until they begin to brown around the edges, 8 to 10 minutes.
Remove the crackers from the oven and cool on racks.
Repeat the rolling and baking process with the remaining dough.
After the crackers have cooled completely, toss them in the salt and cheese powder to coat them lightly, if desired.