Preheat oven to 350 degrees. Line muffin tins with paper liners and set aside.
Measure bran flakes into a liquid measuring cup. Pour milk over top and stir to soak all evenly. Set aside.
In a large bowl, measure flour, brown sugar, baking soda, baking powder, salt, cinnamon, and nutmeg. Stir together to combine. Create a well in the center of the dry ingredients and measure out the wet ingredients into the dry. Stir the wet ingredients together to break up the egg. Then add in the milk-soaked bran flakes.
Slowly incorporate the wet into the dry until the batter comes together. Scoop into prepared muffin tins and bake 20 minutes or until a toothpick comes out clean after being inserted.
Remove to a cooling rack and make the glaze.
For the glaze, stir all ingredients together until runny and smooth. Dip each top of the muffin into the glaze and set back on the cooling rack to let the excess drip down.
Serve immediately or let the glaze set and store for later. Good for up to two days in an airtight container.