Preheat oven to 350 degrees F (175 degrees C). Grease a baking sheet.
Stir flour, bran, baking powder, and salt together in a bowl. Beat egg, sugar, and canola oil in a separate bowl. Stir egg mixture into dry ingredients; beat in enough milk to make a stiff dough. Divide dough into 12 equal pieces and form each piece into a round ball. Place rolls on the prepared baking sheet.
Bake in the preheated oven until golden brown and springy, about 50 minutes.