Preheat oven to 325°F and line an 8 x 8 pan with parchment paper and set aside.
Mix 1 cup each of the flour and sugar, cinnamon, baking soda, nutmeg and salt in large bowl. Add melted butter, 2 of the eggs, 2 teaspoons vanilla extract and carrots; mix well.
Spread 1/2 of the batter into prepared pan. Reserve remaining batter. Set aside
Beat cream cheese and remaining 2/3 cup sugar in another large bowl with an electric mixer until well blended.
Add cream, remaining 1 tablespoon of flour and beat well until blended.
Add remaining 2 eggs, 1 at a time mixing until just blended.
Pour half of the batter on top of the carrot cake batter.
Drop spoonfuls of the cream cheese mixture and reserved carrot cake batter, alternately, over the cheesecake batter in pan. Cut through several times with knife for marble effect.
Bake 50-60 minutes or until toothpick inserted in center comes out clean. Cool in pan on wire rack.
Refrigerate for at least 2 hours or overnight before cutting into squares and serving.