Preheat your oven to 350°F, placing one rack in the center and another at the lowest position. Grease a 9-inch springform pan thoroughly.

In a large mixing bowl, beat cream cheese, granulated sugar, and flour on medium-low speed for 2-3 minutes, until smooth and creamy. Scrape down the sides, then add sour cream, vanilla bean paste, and salt. Gradually mix in eggs, allowing them to incorporate fully without overmixing.

In a separate medium bowl, whisk together the dry ingredients for the carrot cake layer: all-purpose flour, baking powder, baking soda, salt, cinnamon, and nutmeg.

In another bowl, mix together granulated sugar, eggs, melted butter, and vanilla bean paste until smooth. Add the dry mixture, stirring thoroughly, and fold in grated carrots and chopped pecans.

Pour 12 ounces of the carrot cake batter into the prepared springform pan, creating a base. Gently add half of the cheesecake batter on top, ensuring not to swirl it into the carrot layer. Spread the remaining carrot cake batter over this, followed by the rest of the cheesecake batter.

Place the springform pan on a rimmed baking sheet and bake for 55-65 minutes. Check for doneness at 40 minutes and loosely cover with foil if browning too quickly.

Once baked, turn off the oven, crack the door open, and let the cheesecake cool inside for 40 minutes. Then, carefully remove it from the oven and let cool to room temperature for at least 2 hours.

Transfer the cheesecake to the refrigerator for at least 6-8 hours, or overnight if possible.

For the topping, beat cream cheese with unsalted butter until fluffy. Gradually mix in powdered sugar, vanilla bean paste, salt, and whole milk until creamy and smooth.

Spread the cream cheese topping over the chilled cheesecake and garnish with finely chopped pecans.