Preheat the oven to 350 degrees F. Line muffin pans with paper muffin liners.
For the carrot muffins, mix all the dry ingredients in a large bowl. Stir in the egg, vanilla, pineapple, carrot and ginger. Stir in the melted butter last, mix well.
Scoop the batter evenly into 12-14 muffin liners. Bake for 15-20 minutes, until a toothpick inserted into the center of a muffin, comes out clean. Cool completely before glazing.
Place the muffins on a wire rack. In a medium bowl, whisk the powdered sugar, beer and cream together. Use a spoon to drizzle the glaze over the top. Allow the glaze to set before serving.