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Preheat oven to 375u00b0F and line a baking sheet with parchment paper.
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Cut each apple into 16 slices. Chop apple slices into chunks of desired size (I tried to do different sizes, but I mostly stayed on the small side). Spread apples evenly onto baking sheet and bake for 12 minutes or until apples change color and are dry to the touch (see note below on baking times). Set aside to cool completely.
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Increase oven temperature to 425u00b0F. Lightly spray the top of a muffin tin and line with baking cups. (The original recipe states that the cups of the tin should be about 2 3/4 inches across and about 1 inch deep.)
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In a large bowl, sift together flour, baking powder, baking soda, and salt. Mix well.
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In a medium bowl, whisk together sugar, butter, milk, creme fraiche, eggs, egg yolk, and vanilla. Mix until well combined.
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Pour wet ingredients into dry and, using a rubber spatula, gently fold just until mostly moistened. The batter will be lumpy and there should still be some streaks of dry flour.
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Sprinkle apples and grated cheese onto the batter. Gently fold until just combined. Remember, batter will be lumpy so don't try to smooth it out, it will be okay!
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Scoop or spoon (see note below) batter into cups, distributing evenly and filling to the top. Bake for 5 minutes then reduce temperature to 350u00b0F and continue to bake for 10 minutes (they baked for 9 minutes in my oven) until muffins are golden brown and spring back lightly when pressed in the middle. Transfer to a rack to cool.
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Serve warm and top with honey, if desired.
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Notes:
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1. I used 1 large apple but I think you could easily use 1 1/2 - 2 depending on how much apple you like in your muffins.
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2. When baking the apples: Using 1 apple, they were done after 12 minutes. However, if you increase the amount of apples, you may also have to increase the baking time slightly. I recommend starting with 12 minutes and going from there, keeping a close eye on their progress.
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3. For spooning the batter: you can also use an ice cream scoop (the kind that has the ratchet mechanism that measures and releases even scoops) to fill the muffin cups.
