Position the oven racks in the centre and lower third of the oven. Preheat oven to 180 C / Gas 4. Fill a roasting tin halfway with water and place in the lower rack in the oven. Lightly grease the inside of a 23cm springform cake tin.
Beat 675g cream cheese in a bowl using an electric mixer on high speed until fluffy; reduce speed to medium-low. Add caster sugar and beat 2 minutes. Beat 4 eggs, 1 at a time, into cream cheese mixture, beating well before adding the next egg. Beat soured cream and vanilla extract into cream cheese mixture until smooth; add 3 tablespoons flour and beat until cheesecake mixture is smooth.
Beat brown sugar and oil together in a separate bowl using an electric mixer on medium speed until smooth. Add 1 egg and beat for 2 minutes; reduce speed to low. Add 125g flour, cinnamon, baking powder and salt; beat until mixture is combined. Fold grated carrots and walnuts into the mixture.
Spread carrot cake mixture in the prepared cake tin; top with cheesecake mixture. Place tin on the rack above the roasting tin with water in the oven.
Bake in the preheated oven until cheesecake is set, about 1 hour 10 minutes, covering top of the tin with foil if browning too quickly. Cool for 10 minutes.
Run a knife around the edge of the tin to loosen cake; cool to room temperature in tin on a cooling rack. Refrigerate for at least 8 hours. Remove the outside of the springform tin.
Beat icing sugar, 120g cream cheese and almond extract together in a bowl using an electric mixer until icing is smooth. Spread icing on top of cheesecake layer.