Preheat the oven to 375 degrees F. Line a 12-cup muffin pan with paper liners. Whisk the flour, cinnamon, baking powder, baking soda, ground ginger and salt in a large bowl; make a well in the center. Whisk the brown sugar, yogurt, coconut oil, eggs and vanilla in a small bowl; pour into the well in the flour mixture and stir until combined. Fold in the carrots, coconut, macadamia nuts and crystallized ginger.
Divide the batter among the muffin cups, filling them three-quarters of the way. Bake until the muffins are golden and a toothpick inserted into the center comes out clean, 20 to 25 minutes. Let the muffins cool 5 minutes in the pan, then remove to a rack to cool completely.
Meanwhile, make the glaze: Stir the confectioners' sugar with the water in a small bowl. Spread about 1 teaspoon glaze on each muffin and sprinkle with coconut.