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Preheat your oven to 375°F. Lightly grease (or line with parchment) four baking sheets, or as many as you have.
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Beat together the butter, sugars, baking powder, baking soda, and salt.
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Beat in the eggs and vanilla.
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Using a blender or food processor, process the oats with the white chocolate until the oats are finely ground, and the chocolate is mostly ground; a few small chunks are OK.
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Add the oats and flour to the butter mixture, then stir in the peanut butter chips, chocolate chips, and chopped walnuts.
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Drop the dough by tablespoonfuls, 2" apart, onto the prepared baking sheets.
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Bake the cookies for about 12 minutes, until they're just set. They may be barely starting to brown around the edges, but the tops won't be brown at all.
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Remove the cookies from the oven, and cool.
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Yield: 5 dozen cookies.