Preheat oven to 450F (225C). Spray 12-cup muffin tin with non-stick spray or line with muffin liners.
In a large bowl, mix together flour, baking soda, ginger and cinnamon. Set aside.
In a microwave-safe bowl, heat the molasses and butter/oil until melted. Stir until thoroughly mixed together and set aside.
In another bowl, whisk together the brown sugar, egg, yogurt and milk. Pour into the butter & molasses mixture and whisk until everything is incorporated.
Pour wet ingredients into dry and mix until 'just' combined. Do not overmix but be aware the batter will be very thick and lumpy.
Fill the muffin tins to the very top and bake for 5 minutes at 450F. Keeping the muffins in the oven, reduce the temperature down to 375F (190C) and continue to bake for 15 more minutes. Muffins are finished when a toothpick inserted into the centre comes out clean.
As the muffins cool, prepare the glaze with 1 cup icing sugar, 1/2 tsp vanilla and enough milk to make the desired consistency. Either dip the muffins into the glaze, or drizzle on top.