Preheat the oven to 175 degrees. Line a 12-compartment muffin tin with paper inserts, brush with butter and lightly dust with flour. Peel and grate the carrots. Chop walnuts coarsely if using them.
Combine flour, baking soda, salt, cinnamon, nutmeg and ginger in a medium bowl. Beat sugar and butter in a large bowl with a mixer. Add eggs and beat. Add flour mixture and stir until mixture is homogeneous. Stir in carrots, walnuts, and raisins, if used.
Divide the dough among the paper inserts, filling every 3/4.
Bake muffins for 14 to 18 minutes. Allow to cool in the pan for 5 minutes, then let cool completely on a rack.
Meanwhile, prepare the creamy frosting. In a bowl with a mixer, beat all the icing ingredients with a mixer on medium speed. Put the icing in the refrigerator for 10-20 minutes. decorate the cooled carrot muffins with cooked glaze.