In a large bowl beat together all the ingredients of the dough until smooth and soft, about 4 minutes. Place the dough in a lightly greased bowl. Cover with plastic wrap and place in the warmest place in your kitchen. Let the dough rise until it doubles in size. The time the dough takes to rise depends of how warm is your kitchen. It may take longer than one hour.
Deflate the dough and roll into a 14x20-inch rectangle.
Spread 4 tablespoons of softened butter over the rolled dough. In a small bowl, mix sugar, cinnamon, ginger, and cloves. Sprinkle the mixture over the dough. Sprinkle on top of the sugar mixture the shredded carrots, walnuts, and pineapple.
Tightly roll the dough into a log. Evenly cut into 12 pieces.
Place the pieces in a slightly buttered 9x13-inch baking dish. Cover with plastic wrap and allow the rolls to rise until they are nearly doubled in size, about 40 minutes. While they are rising, preheat oven to 375°F.
Bake for 15 minutes or until golden brown. Remove from oven.
In a large bowl, beat all the ingredients of the icing until well combined. Spread the icing on top on the rolls and serve.