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Preheat oven to 425 F.
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Prepare a 12 cup muffin pan with paper muffin cups.
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Make the crumb topping: Add the crumb topping ingredients in a small mixing bowl. Work the butter into the dry ingredients with a pastry blender, a fork or even your fingers until the mixture holds together in a clump if you press it together with your fingers. This can take a little bit of time. If you melt the butter, it will change the whole consistency. Just work the butter in. You should have no dry ingredients still powdery in the bowl at the end. Cover and set aside in the refrigerator until ready to use.
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Make the muffin batter: In a large bowl, combine flour, cinnamon, nutmeg, baking powder, baking soda, and salt.
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In another separate bowl, add the eggs, milk, brown sugar, applesauce, and yogurt. Whisk until well combined.
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Pour the wet mixture into flour mixture and stir only until combined. Do not over stir!
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Then, peel and dice the apples. Add 3/4 of the diced apples into the batter and gently fold the apples into the batter.
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Scoop into prepared muffin pan until the cups are almost full.
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Add the remaining diced apples onto the top of the batter, gently and only slightly pressing them into the batter.
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Pile crumb topping on top of the apples.
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Bake at 425 F for 5 minutes, then immediately lower the heat to 375 F. Do NOT open the oven. Bake for an additional 15-18 minutes or until toothpick inserted in center comes out fairly clean. Over baking will result in dry muffins.
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Allow to cool in pan for 10 minutes, then carefully remove from pan onto a rack for cooling.