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Preheat oven to 350° and place rack in center of oven. Grease and flour two 9 inch cake pans.
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In large mixing bowl, blend cake mix, milk, butter, eggs and vanilla with electric mixer on low for 1 minute. Scrape bowl and mix on medium for 2 minutes.
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Pour batter into prepared pans and bake 27-29 minutes.
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Cool in pans for 10 minutes; remove to rack and cool for 30 minutes.
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To prepare frosting, place butter and brown sugars in a medium saucepan over medium heat, stirring, until mixture comes to a boil.
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Add milk, stir and bring back to a boil; remove from heat.
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Mix in powdered sugar and vanilla with wooden spoon until smooth.
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Frost cake layers while frosting is still warm, working quickly (frosting will set as it cools). If frosting gets too hard to work with, warm over low heat for 1 minute, stirring constantly.