In a large bowl, combine 4 peeled and grated carrots, 2 peeled, cored, and grated apples, 1 cup of raisins, and 1 cup of fine bread crumbs.
In a separate small bowl, sift together 1 1/2 cups of all-purpose flour, 2 teaspoons of baking powder, 2 teaspoons of ground cinnamon, 1 teaspoon of baking soda, 1 teaspoon of salt, 1 teaspoon of ground nutmeg, and 1 teaspoon of ground allspice.
In another large bowl, cream together 2/3 cup of butter, 1/2 cup of white sugar, and 4 eggs.
Gradually stir in the sifted flour mixture into the butter mixture.
Add the carrot and apple mixture to the batter and mix well.
Transfer the mixture to a lightly greased 2-quart mold.
Place a steamer rack in the bottom of a large, deep pot and set the filled mold on top of the steamer rack.
Pour enough water into the pot to cover the bottom 2/3 of the mold.
Bring the water to a boil over medium heat, then reduce heat to low and cover the pot.
Simmer for 2 hours and 45 minutes, adding water occasionally to maintain the water level.
Remove the pudding from the water and allow it to cool for 10 minutes before turning it out of the mold onto a plate.