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Beat together Eggs, sugar, applesauce and oil.
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Add carrots, vanilla and cinnamon and continue mixing on Medium speed.
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In a separate bowl; mix together flour, baking soda, baking powder and salt.
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Slowly add the flour mixture into the cake batter.
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Continue mixing on Medium speed for around 2 minutes.
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Add cake batter to a floured/greased bundt pan.
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Prepare cheesecake mixture:
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Beat together egg and sugar; add softened cream cheese and beat until smooth.
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Evenly pour the cream cheese mixture over the top of the carrot cake batter.
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Using a butter knife; cut cheesecake mixture into cake batter until a marble effect is created.
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Bake at 325 Degrees for 55 minutes-1 hour until a toothpick comes out clean.
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Allow cake to cool completely.
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Prepare Maple Glaze:
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Melt butter in a small saucepan on medium heat.
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Mix in maple syrup and cinnamon.
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Whisk in confectioners sugar.
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Continue whisking until clumps disappear over medium heat.
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Pour the warm glaze over the cake.