In your largest mixing bowl, place the wheat bran. Use a big bowl, because by the end, all the batter will be in this bowl. Make a well in the centre and add the buttermilk.
Mix the buttermilk and bran together and let it stand for ten minutes, while you prepare the rest of the ingredients. In another bowl, whisk together the flour, baking soda, baking powder and salt. Add the nuts and apricots. Toss them together to coat the fruit in flour. This will prevent the fruit from sinking to the bottom of your muffins.
In a third bowl, put the sugar, oil, egg, apple sauce and almond extract. whisk thoroughly.
Add the wet ingredients to the bran mixture and combine well.
Add the dry ingredients to the large bowl and fold together with a spatula. You don't need to mix too much, just fold it together until the flour is gone.
Spoon the mixture into prepared muffin cups. Bake in the top half of the preheated oven at 375F for 20-25 minutes. (Mine come out perfect at 22 minutes.)
Check for doneness by seeing if a toothpick comes out clean when you poke a muffin.
Let them cool on a rack before you pack them away.