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Set oven to 350 degrees.
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Set oven rack to second-lowest position.
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Grease a 13 x 9-inch baking pan.
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To make the cheesecake topping: in a food processor, blend all ingredients for 1 minute until smooth; remove to a bowl.
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In the processor without cleaning the bowl, add in 1/2 cup butter and 1-1/3 cups sugar; blend until smooth (about 1 minute).
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Add in vanilla, lemon extract, eggs, sour cream and blend well (about 30 seconds).
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Add in flour, salt, baking powder, baking soda; blend to make a smooth batter (about 30 seconds).
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Spoon batter into prepared baking pan.
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Spoon on cream cheese mixture topping (don't worry if there are open spaces).
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Drop jam dollups by teaspoonfuls over cake and cream cheese areas.
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Swirl the jam and the cream cheese topping to make a gentle marble effect.
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Bake for 35-40 minutes, or until cake is set and the topping seems dry.
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Cool completely and dust with powdered sugar.