Position the oven racks in the center and lower third of the oven. Fill a roasting pan halfway with water and place on the lower rack. Preheat the oven to 350 degrees F (175 degrees C). Grease a 9-inch springform pan with cooking spray.

Make the cheesecake: Beat cream cheese in a large bowl with an electric mixer on high speed until fluffy; reduce speed to medium-low. Add white sugar and beat for 2 minutes. Beat in eggs one at a time, mixing well after each addition. Mix in sour cream and vanilla until smooth. Stir in flour and set cheesecake batter aside.

Make the carrot cake: Beat together brown sugar and oil in a separate large bowl with an electric mixer on medium speed until smooth. Add egg and beat for 2 minutes; reduce speed to low. Mix in flour, cinnamon, baking powder, and salt until combined. Fold carrots and walnuts into batter.

Spread carrot cake batter into the prepared pan; top with cheesecake batter. Place the pan on the center rack above the roasting pan with water.

Bake in the preheated oven until the cheesecake is set, about 1 hour and 10 minutes, covering the top with aluminum foil if browning too quickly. Allow to cool for 10 minutes.

Run a knife around the edge of the pan to loosen the cake; cool to room temperature in the pan on a wire rack. Place in the refrigerator for at least 8 hours to overnight.

Make the frosting: Beat confectioners' sugar, cream cheese, and almond extract in a medium bowl with an electric mixer until smooth.

Remove the ring of the pan. Spread frosting on top of the chilled cheesecake layer.