Preheat the oven to 350°F (175°C). Prepare an 8-inch springform pan by lining the bottom with parchment paper and spraying the sides with non-stick spray.

In a stand mixer, beat the softened cream cheese for 5-6 minutes until fluffy. Gradually add ½ cup granulated sugar and 2 tablespoons flour, mixing until combined.

Incorporate the eggs one at a time, mixing well after each addition. Mix in 1 teaspoon vanilla extract and ¼ cup heavy cream. Blend on high speed for 2-3 minutes.

Pour the cheesecake batter into the prepared pan. Bake for 10 minutes. Lower oven temperature to 200°F (93°C) without opening the oven and bake for another 55-60 minutes until center jiggles slightly.

Cool for 15 minutes in the oven, then transfer to a wire rack and chill in refrigerator for at least 2 hours or overnight.

In another bowl, cream together ¾ cup softened butter, ½ cup brown sugar, and ½ cup granulated sugar until fluffy.

Gradually add 3 eggs, mixing one at a time. Combine with the dry ingredients: 1 ½ cups flour, 2 teaspoons baking powder, 1 ½ teaspoons baking soda, 1 teaspoon salt, and 2 teaspoons cinnamon. Fold in 1 cup grated carrots.

Spread carrot cake batter over the chilled cheesecake layer and bake at 350°F for 30-35 minutes or until a toothpick comes out clean.

Cool the entire cake on a wire rack.

Beat together 1 package of softened cream cheese, 1 teaspoon of vanilla extract, and 3 tablespoons of heavy whipping cream. Gradually sift in powdered sugar to desired consistency.

Frost the cooled cake and sprinkle with crushed pecans if desired.