2 cups all-purpose flour
2 teaspoons baking powder
2 teaspoons baking soda
2 teaspoons ground cinnamon
¾ teaspoon salt
3 cups grated carrots (you can grate the carrots in a food processor fitted with a shredding blade)
1 cup coarsely chopped walnuts or pecans
1 cup shredded coconut, sweetened or unsweetened
½ cup moist, plump raisins (dark or golden) or dried cranberries
2 cups sugar
1 cup canola or safflower oil
4 large eggs

For the frosting:

8 ounces cream cheese, at room temperature
1 stick (8 tablespoons) unsalted butter, at room temperature
1 pound (3 3/4 cups) confectioners
1 tablespoon fresh lemon juice or 1/2 teaspoon pure lemon extract
½ cup shredded coconut, optional
Toasted finely chopped nuts and/or toasted coconut, for topping, optional