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Preheat oven to 350 degrees F. Line two baking sheets with parchment paper and set aside.
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Whisk together the flour, baking soda and salt; set aside.
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On medium speed, cream together the butter + peanut butter + granulated sugar + brown sugar + vanilla extract for about 3 minutes. Add the egg and beat to combine. On low speed, gradually add the flour until just combined. Stir in the oats, and then the chopped nuts.
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Using a large ice cream scoop or a spoon, drop dough onto prepared baking sheets about 2 inches apart.
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Bake for 13-15 minutes, or until the cookies are lightly golden. Cool completely on the baking sheet and then store in an airtight container at room temperature.