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Mix wheat bran and buttermilk in large bowl. Let stand for 10 minutes.
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In a seperate bowl, mix oil, egg, sugar, and vanilla. Add to buttermilk mixture.
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In another bowl, combine the flour, baking soda, baking powder, cinnamon, nutmeg, and salt. Mix into buttermilk mixture.
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Chop up apples into really small chunks and fold into mixture.
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Spoon batter into prepared muffin tins and bake at 375 for 15 to 20 minutes.