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Preheat oven to 350 and prep your 2 baking sheets by lining them with parchment paper.
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In a medium bowl, mix together flour, oats, baking powder, baking soda, salt, cinnamon, and nutmeg. Set aside.
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In a large bowl, cream together the butter and sugars (by hand or with a hand mixer). Add the egg, apple sauce, and vanilla and mix until smooth.
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Add the flour/oats mixture a little at a time into the large bowl and stir by hand until well combined. Then, add the diced apples and stir.
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If the mixture seems too moist, add just a little bit of extra flour or oats.
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Use 1 tablespoon of dough to make each cookie and drop onto the prepped baking sheets about 2 inches apart. I measured and dropped messily onto the sheet, moving quickly. Then, before baking, I went back and shaped the cookies into more round cookie form.
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Bake for 10-12 minutes, or until the edges become a light, golden brown.
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Cool on baking sheet for 2 to 3 minutes and move to a wire rack to cool completely.