Begin by preheating your oven to 350 degrees Fahrenheit (175 degrees Celsius) and positioning the racks in the center and lower third of the oven. To ensure even cooking, fill a roasting pan halfway with water and place it on the lower rack.
Next, grease a 9-inch springform pan with cooking spray to prevent the cake from sticking. This will make it easier to remove the cake from the pan once it's fully cooked.
In a large bowl, beat cream cheese with an electric mixer on high speed until it becomes fluffy. Reduce the speed to medium-low and add white sugar, beating for 2 minutes. Then, add eggs one at a time, mixing well after each addition. Mix in sour cream and vanilla extract until the batter is smooth. Finally, stir in flour to complete the cheesecake batter.
In a separate large bowl, beat together brown sugar and oil with an electric mixer on medium speed until smooth. Add an egg and beat for 2 minutes before reducing the speed to low. Mix in flour, cinnamon, baking powder, and salt until combined. Fold in the carrots and walnuts to create the carrot cake batter.
Spread the carrot cake batter into the prepared pan and top it with the cheesecake batter. Place the pan on the center rack above the roasting pan with water and bake for about 1 hour and 10 minutes, covering the top with aluminum foil if it begins to brown too quickly. Allow the cake to cool for 10 minutes before running a knife around the edge of the pan to loosen it. Cool the cake to room temperature on a wire rack and refrigerate for at least 8 hours, or overnight.
To complete the dessert, beat together confectioners' sugar, cream cheese, and almond extract in a medium bowl with an electric mixer until smooth. Remove the ring of the pan and spread the frosting on top of the chilled cheesecake layer.
