Preheat your oven to 425°F (218°C). Grease a 12-cup muffin pan well or line it with paper liners.
Cut the butter into small pieces so it melts evenly. Microwave the butter and molasses together in a large bowl for about 1 minute, then whisk until completely smooth. Set aside to cool slightly while you mix the dry ingredients.
In a separate bowl, whisk together the flour, baking soda, salt, cinnamon, ginger, and cloves until evenly combined.
Whisk the brown sugar, egg, yogurt, and milk into the cooled molasses mixture until smooth.
Pour the wet ingredients into the dry ingredients and stir just until combined. The batter will be thick and a little lumpy. Divide the batter evenly among the muffin cups, filling each all the way to the top. Sprinkle with coarse sugar if you're using it.
Bake at 425°F (218°C) for 5 minutes, then, without opening the oven, reduce the temperature to 350°F (177°C) and bake for another 15 to 16 minutes, until the tops are cracked and a toothpick inserted in the center comes out clean.
Let the muffins cool in the pan for 5 to 10 minutes before glazing. They should still be warm when the glaze goes on.
Whisk together the confectioners' sugar, lemon juice, and milk until smooth. Add a little more sugar if it's too thin, or more milk if it's too thick. Drizzle generously over the warm muffins.