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Preheat oven to 350F.
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Put walnuts in a food processor and process until ground. Transfer to a mixing bowl and add flour, salt, baking powder, and cinnamon; stir to combine.
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Beat powdered sugar and butter at high speed with a electric stand mixer 4 minutes or until light and fluffy. Add egg and vanilla, and beat until combined. Add flour mixture, and beat at medium speed 30 seconds.
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Drop batter by tablespoonfuls 2 inches apart on a parchment-lined baking sheet. Dip finger in cold water, and press into each cookie, forming an indentation. Fill each indentation with ½ teaspoon apple butter. Smooth out any peaks in apple butter.
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Bake in preheated oven for 15 - 17 minutes or until the edges just begin to brown. Transfer to wire rack and cool completely. Repeat with remaining cookie dough.