Combine the warm water, brown sugar, salt, softened butter and yeast in a large bowl. Stir in the whole wheat flour until combined well. Add the bread flour, ½ cup at a time, mixing well after each addition.
Form the dough into a ball and turn out onto a floured surface. Add more flour, 1 to 2 tablespoons at a time, if the dough is too sticky to work with. Knead for about 7 minutes, until smooth and elastic. Place in a greased bowl, turn the dough over to lightly grease all sides, and cover with a plate. Let rest for 1 to 1 ½ hours in a warm spot, until doubled in size.
While the dough proofs, butter two 8-inch by 4-inch metal loaf pans. If vegan, use oil to grease the pans.
Punch down the dough. Turn out onto a floured surface and cut the dough into two halves. Flatten the first half into a rectangle, approximately 8 inches by 6 inches. Beginning at a 6-inch side, roll up the dough and push in the sides gently, until you have formed an even log. Repeat with the second half of the dough. Place the formed loaves in the pans, seams down, and tuck the ends under the loaves.
Cover the loaves with the dishtowel. Let rest in a warm spot for about an hour until they puff up above the edge of the pan.
About 15 minutes before the bread is ready to bake, preheat the oven to 425°F. Bake the loaves for 25 to 30 minutes or until browned on top and the bottom of the loaves sound hollow when you tap them. Remove the loaves from the pans and cool completely on a wire rack before slicing.
Store bread in a clean cloth produce bag.