2. Place the butter in a mixing bowl and beat at high speed with an electric mixer for 30 seconds. Gradually add the brown sugar and continue to beat until the mixture is very fluffy.
3. With the mixer on low speed, add the egg and egg white. Stir in the cinnamon, nutmeg and carrots.
4. Sift the flour, baking powder and salt together.
5. Fold in half the flour mixture. Stir in the pineapple, raisins and walnuts. Fold in the rest of the flour mixture. The batter should be smooth, but do not overmix.
6. Coat a 10-inch round cake pan with nonstick spray. Pour the batter into the pan. Bake until the cake is golden brown and set in the center, about 35 minutes. Allow the cake to cool for 10 minutes before removing it from the pan.
For the cream cheese icing:
1. In a small mixing bowl, beat the cream cheese, confectioners' sugar, lemon zest, lemon juice and vanilla together until the mixture is smooth.
2. Using a spoon or spatula, spread the icing on top of the cooled cake. Store the cake in the refrigerator in an airtight container. Cut the cake into 12 pieces and allow it to come to room temperature before serving.