Preheat oven to 350F; line a muffin tray with paper liners.
Combine the butter, coconut sugar, molasses, cottage cheese, milk, egg, and vanilla extract in a food processor or blender and process until smooth. Let it sit for 2 minutes.
Meanwhile, whisk together the flour, baking soda, salt, ginger, cinnamon, allspice, and cloves.
Add the wet ingredients to the dry all at once and use a wooden spoon to combine, being careful not to over-mix.
Fill each muffin well about 2/3 full of batter and bake until a toothpick inserted inside comes out clean or with just a couple crumbs, about 16 to 18 minutes. Cool completely.
Once the muffins have cooled, make the glaze. Whisk together the powdered sugar, vanilla, and enough water so it reaches your desired consistency.
Drizzle the glaze on the cooled muffins and allow it to set before serving.