That being said: when the going gets tough, the tough BAKE!
No eggs? No problem. The following Early American Brown Brown recipe is from Where's Mom Now That I Need Her by Betty Rae Frandsen, Kathryn J. Frandsen and Kent P. Frandsen. It's easy and I've made it successfully with nothing but all-purpose flour in the past. It's a dense bread with a touch of sweetness. Enjoy!
Early American Brown Bread
2 cups whole wheat flour
3/4 cup white flour
1 cup brown sugar, packed (I used light brown sugar)
2 teaspoons baking soda
1/2 teaspoon salt
2 cups milk
4 teaspoons lemon juice or vinegar (I used white vinegar)
Mix whole wheat flour, white flour, brown sugar, baking soda and salt in a large bowl. Combine milk and lemon juice or vinegar; let stand for 10 minutes. Stir milk gradually into flour mixture until well blended. Spoon batter into greased loaf pan. Bake at 350 degrees F for 1 hour.