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Preheat oven to 350 degrees F.
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In large mixing bowl, combine diced apple, applesauce, Greek yogurt, molasses, vanilla extract, coconut sugar, white sugar, eggs and olive oil. Mix well until smooth and combined.
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Add cinnamon, salt, wheat bran, flour and baking powder. Stir just until batter comes together. Do not overmix.
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Line muffin tin with paper liners and fill each cup about 3/4 full.
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Bake for 30–40 minutes, depending on your oven, until toothpick inserted in center comes out with moist crumbs.
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Cool slightly, then serve with spoonful of Greek yogurt or smear of butter.