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Assemble ingredients.
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Grease muffin tins or spray with a no-stick cooking spray. Be sure to grease or spray the entire top of the muffin pan as well. Alternatively, line each muffin cup with a paper liner.
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Preheat oven to 500°F (then drop it back to 400°F when muffins are placed in oven).
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Break eggs into bowl. Whisk. Add applesauce, sour milk, molasses, brown sugar, vanilla, and orange rind. Whisk together well. Add the bran. Stir until completely incorporated. Set aside for about 10 minutes.
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Meanwhile, in large bowl, combine flours, baking powder, soda, cinnamon, allspice, and salt. Whisk to combine ingredients.
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In separate bowl, cream shortening well. Pour the wet bran mixture into the bowl and stir well, or whisk, to blend in the shortening. Mixture will be lumpy.
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Add wet bran mixture and raisins to the dry ingredients. With a wooden spoon, gently stir mixture just until flour is incorporated. Do not overmix.
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Using an ice cream scoop or a small ladle, fill muffin tins to top of rim. Reduce oven heat from 500°F to 400°F and place muffins in oven. Bake 15-20 minutes or until muffins spring back to a light touch or a cake tester inserted into the center of the muffin comes out clean. Let cool in pan for 5-7 minutes then transfer to a wire rack to finish cooling.