Preheat oven to 350 degrees F. Spray two 9x2-inch round metal cake pans with flour-added baking spray. If you are using dark cake pans, preheat the oven to 325 degrees F.
Shred carrots. Toss them with the 1 cup granulated sugar and place in a colander set over a large bowl. Let sugared carrots sit for about 20 minutes to drain. Press occasionally, draining out liquid until you've collected 1 cup (no need to keep it, just throw it out).
Meanwhile, melt butter in a saucepan set over medium heat. Cook it until it develops a nutty aroma and starts to turn brown right around the edges. Pour the browned butter into a mixing bowl and let it cool for 2 minutes.
Add the dark brown sugar to the butter and stir well. Stir in eggs, one by one, then stir in vanilla.
In another bowl, stir together the flour, baking powder, baking soda, salt and cinnamon. Add the flour mixture to the butter mixture and stir until incorporated. Stir in the sugared carrots, drained pineapple, walnuts and raisins.
Divide the batter evenly between the cake pans and cook for 40-50 minute or until the cakes test done. If using two racks, switch racks halfway through so that both cakes cook evenly. Note: My cakes were done in 40 minute and I used dark pans and 325 degrees F, so check at 40 minutes.
Cool the cakes on a rack for 10 minutes, then turn from pan and cool completely. Prepare icing. Beat together cream cheese and butter. Stir in sugar, vanilla and lemon juice. If you'd like some extra tartness, stir in a bit of sour cream. Beat until light and fluffy. Frost cake.