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Chocolate Batter: Melt chocolate with butter in the microwave (2 minutes at power 7).
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Beat eggs until foamy.
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Gradually add sugar.
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Continue beating at medium speed of the electric mixer until thick and lemon coloured, about 5 minutes.
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Add vanilla and chocolate mixture.
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Add flour, baking powder and salt, Mix well.
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Cream Cheese Batter: Beat cream cheese with butter, sugar, eggs and vanilla until well blended.
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To finish brownies, layer half of the chocolate batter in a greased and floured 8-inch square pan. Spread with the cream cheese batter.
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Top with spoonfuls of the chocolate batter. Swirl a knife through the layers to marble.
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Bake at 350F in a preheated oven for 30-35 minutes, or until brownies pull away from the sides of the pan. Cool on a wire rack.