Preheat your oven to 325°F (163°C) and prepare a 9-inch springform pan by greasing the sides and lining the bottom with parchment paper.

In a large mixing bowl, beat 16 ounces of room-temperature cream cheese and 1 cup of granulated sugar until smooth, about 3 minutes. Add 3 room-temperature eggs one by one, mixing thoroughly. Blend in 1 cup of sour cream.

In another bowl, whisk together 2 cups of all-purpose flour, 1 teaspoon of baking powder, 1 teaspoon of baking soda, 2 teaspoons of cinnamon, and a pinch of nutmeg.

Fold in 2 cups of freshly grated carrots into the dry ingredients.

Spoon dollops of both the cheesecake and carrot cake batters into the prepared springform pan, alternating between the two, and swirl together with a knife or skewer.

Prepare a water bath by placing a larger roasting pan filled with hot water in the oven alongside the cheesecake. Bake for 60-70 minutes until the center is set.

After baking, turn off the oven and leave the cheesecake inside with the door slightly ajar for about an hour to cool. Then, transfer to a wire rack to cool completely and refrigerate for at least 4 hours.

For the frosting, mix softened cream cheese and powdered sugar until smooth, then spread it over the chilled cheesecake and sprinkle with chopped pecans.