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Preheat oven to 350 degrees.
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Mix first 3 ingredients together in a small bowl.
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In another bowl, cream butter and peanut butter together.
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Add both sugars and mix well.
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Add eggs and vanilla to the wet mixture.
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Incorporate the flour mixture, then add the oats.
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Using an ice cream scoop (yes, THAT big!), place balls of dough 3 inches apart on parchment lined cookie sheets.
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Bake about 10 min, or until cookies have spread and edges are just turning golden brown.
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Remove from oven and let cool on cookie sheet for 5-10 min before removing to wire rack.
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If you're going to make PB cookie sandwiches:.
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Mix the three icing ingredients together.
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Spread a thin layer on the underside of one cookie.
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Sandwich another cookie on top.