In a large mixing bowl, sift together the whole wheat and all purpose flours, baking soda, salt, and brown sugar.
Make a well in the center of the dry ingredients and pour in the buttermilk. With a spoon, or your hands, mix everything together until a sticky dough forms. You can add a small splash of extra liquid if your dough seems too dry.
Transfer the dough to a lightly floured surface and knead it about 4-5 times until it a bit smoother and less sticky.
Roughly shape the dough into a fat disk about 8 inches across. With a sharp knife, cut two slashes, about 1/4" deep, into the top of the loaf in the shape of an X. Transfer to a baking sheet.
Bake for 15 minutes, then turn the oven down to 400F and bake for 15-20 more minutes. The bread should be puffed up, golden brown, and sound hollow when tapped on the bottom when done.