Preheat the oven to 350°F (176 °C). Generously butter the muffin tins.
In a large bowl, sift the flours, bran, sugars, allspice, baking powder and soda, salt, and cinnamon. Stir in the carrots.
In a small bowl, whisk together the melted butter, buttermilk, and egg and whisk until thoroughly combined.
Using a spatula, mix the wet ingredients into the dry ingredients and stir to combine.
Scoop the batter into 8 muffin cups using a spoon or an ice cream scoop. The batter should be slightly mounded above the edge. Sprinkle the streusel topping evenly over the mounds of batter and press it into the batter slightly.
Bake the muffins for 32 to 35 minutes, rotating the pans halfway through. The muffins are ready to come out when they smell nutty and their bottoms are a dark golden-brown (you can twist a single muffin out of the pan to check).
Remove the tins from the oven, twist each muffin out, and place it on its side in the cup or on a wire rack to cool. Best eaten warm from the oven or later that same day. They can also be kept in an airtight container for up to 2 days or frozen and reheated.