Preheat oven to 350 degrees. Line a 12-cup muffin pan with paper liners.
Spread the wheat bran on a baking sheet, and toast in the oven for 6 to 8 minutes, making sure to stir or shake it around periodically. Let cool.
In a large bowl, mix together the applesauce, soymilk, water, and brown sugar.
Stir in the oil, egg, and egg white. Then mix in the toasted bran.
In a small bowl, mix together the flours, baking powder, baking soda, and salt. Sift the dry ingredients into the wet ingredients.
Stir just until combined, and then stir in the pecans.
Spoon the batter into the muffin pans, filling almost to the top. Sprinkle rolled oats on top of each muffin, if desired.
Bake for 20 to 25 minutes, or until muffins feel set in the center.
Serve with honey butter, if desired. (To make honey butter: Beat 1 stick of softened butter in bowl of stand mixer, and drizzle in 1/4 cup honey. Continue beating until combined. Use at room temp, but store in fridge.)