Preheat the oven to 180°C (356°F). Grease or line a 12 muffin tray.
Melt the butter, then add it to a bowl and let it slightly cool. Add in the brown and white sugar and the molasses and mix it together. Beat in the egg.
Mix in the grated zucchini.
In a separate bowl mix together the flour, baking powder, baking soda, salt and spices so that there are no lumps.
Add half the flour mixture to the zucchini mix, along with half the milk and fold it gently. Then add the remaining flour and milk. Fold it very gently until just combined.
Scoop the mixture evenly into the 12 muffin tray. Bake the muffins for 16-18 minutes until the top of the muffin springs back when touched, or a skewer inserted in a muffin comes out clean.
Remove the muffins from the tray and allow them to cool.
Once the muffins have cooled, make the glaze by mixing the ingredients together into a thick but droppable paste. You may need to add more icing sugar or milk as needed. Drizzle the glaze over the muffins.
Notes
I use NZ cup sizes, which are larger than US cups. If you have a smaller cup, it is best to use the gram amounts listed instead to avoid any over or under measuring.