Preheat the oven to 400°F. Line a 12-cup muffin tin with paper liners, or lightly grease the tin. Set aside.
In a large bowl, combine the bran, flour, both sugars, cinnamon, baking powder, baking soda, and salt. Stir to combine.
In a medium bowl, whisk together the pumpkin purée, egg and egg yolk, yogurt, and oil. Add this to the large bowl of dry ingredients and mix to just combine. Do not overmix. Transfer the batter to the muffin tin.
Bake for 20 to 25 minutes, or until the muffins are golden brown and spring back to the touch. Remove from the oven and let cool on a cooling rack before icing.