Combine whole wheat flour, all-purpose flour, soy flour, brown sugar, baking powder, baking soda, and salt in a large mixing bowl. Whisk buttermilk and egg whites into the flour mixture until no clumps remain in the resulting batter; add mashed bananas and mix well.
Place a large non-stick skillet over medium heat. Add 1/4 teaspoon oil to the hot skillet; tilt skillet to coat cooking surface in oil. Ladle about 1/4 cup batter into the skillet. Cook until tiny air bubbles form on top, 2 to 5 minutes; turn and continue cooking until the bottom is browned, 2 to 3 minutes. Repeat with remaining oil and batter. Keep finished pancakes warm.