Preheat the oven to 350 degrees F (175 degrees C). Line a muffin pan with paper liners.

Combine flour, rhubarb, brown sugar, wheat bran, baking powder, cinnamon, and nutmeg in a large bowl.

Mix applesauce, oil, molasses, vinegar, and vanilla extract together in a separate bowl. Pour over flour mixture. Slowly mix until a thick batter forms. Divide batter among the muffin cups.

Bake in the preheated oven until a toothpick inserted into the center comes out clean, 15 to 20 minutes.