Preheat oven to 400°F (200°C). Grease a regular-sized muffin pan with butter or line with 12-15 cupcake liners.
In a large mixing bowl, beat butter and both sugars. Beat in the eggs, then beat in the banana. In a medium-sized bowl, whisk together the flours, baking powder, baking soda and salt and add it to the banana mixture, along with the buttermilk and vanilla and mix until combined. Stir in ¾ of the nuts.
Divide batter among the muffin cups and sprinkle with remaining nuts. Bake for about 15 minutes, until a toothpick inserted in the center of a muffin comes out clean.
Cool in the pan on a wire rack for 5 minutes. Remove from the pan and cool completely.
Store in an airtight container for up to three days. Banana Muffins can also be frozen for up to two months.