Position the oven racks in the center and lower third of the oven. Fill a roasting pan halfway with water and place onto 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. Add sugar and beat on medium-low speed 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 aside.

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

Spread carrot cake batter evenly into the prepared pan, then pour cheesecake batter over top.

Place cake into the preheated oven on the center rack (above the roasting pan with water). Bake until cheesecake is set, about 1 hour and 10 minutes, covering the top with aluminum foil if browning too quickly. Remove from the oven, place onto a wire rack, and let cool for 10 minutes.

Run a knife around the edge of the pan to loosen cake, then let cool to room temperature, about 50 minutes. Cover with foil and refrigerate until completely chilled, 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.

Uncover the cheesecake and carefully remove the ring of the pan. Spread frosting on top of chilled cheesecake layer. Decorate with chopped walnuts, if desired.