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In a medium saucepan, melt the butter over medium heat until melted. Remove from the heat.
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Add the dark brown sugar and granulated sugar and stir until sugars are incorporated and smooth. Chill the mixture for 10 minutes.
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Remove from the refrigerator and stir in the egg, egg yolk, and vanilla.
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Add the flour, oats, baking soda, 1/2 teaspoon salt, and cinnamon and mix together. Stir in the white chocolate chips and chocolate chips.
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Roll by hand into 24 medium-size balls or use a scoop, and place on a light-colored cookie sheet. Chill for at least 30 minutes.
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Preheat the oven to 325 degrees F. Remove the cookies from the refrigerator and bake for 12 to 14 minutes.