Preheat oven to 375 F°. Line 12 standard muffin cups with paper liners, set aside.
In a medium bowl, whisk together flours, wheat bran, baking powder, baking soda, salt, cinnamon, and brown sugar.
In a large bowl, whisk eggs, pumpkin puree, oil, and applesauce until combined.
Stir the flour mixture into the wet ingredients, mixing until just combined. Add mashed carrots and stir until evenly distributed, being careful not to over mix.
Evenly divide the batter between muffin cups, filling about 2/3 full. Bake for 15-18 minutes, until a toothpick inserted into the center of the muffins comes out without raw batter on it. Cool in muffin pan for 10 minutes, then remove muffins from the pan to continue cooling.