In a large bowl, combine warm water, brown sugar, and honey. Sprinkle in yeast and wait until mixture bubbles. Stir in milk, salt, cumin, shortening, and egg. Add white flour and stir. Gradually add whole-wheat flour until dough is easy to handle. (Whole wheat bread rises better if it's not too dry.)
Turn dough onto a lightly floured board and knead until smooth and elastic. Place in oiled bowl, turn oiled side of dough up and let rise in a warm place until doubled in size, about 1 hour.
Punch dough down and flatten into a round. Roll lightly and place in a greased round loaf pan. Oil top of loaf lightly. Let rise until doubled.
Preheat oven to 375 degrees F. Bake until golden brown and loaf sounds hollow when tapped, about 40 to 45 minutes. Cool on wire rack.