Preheat the oven to 175 degrees. Place the muffin inserts in the 18-compartment muffin tin. Beat the vegetable fat and sugar with an electric mixer in a medium bowl. Set aside.
Sift flour and salt together into a large bowl. Set aside. Combine eggs, buttermilk, vanillin, baking soda, and vinegar in a separate bowl.
Add flour mixture and cream mixture to the sugar mixture, whisking after each addition. Beat the mixture until smooth.
Place the dough in the prepared muffin insert. Bake the muffins for 17 – 20 minutes. Remove muffins from oven, remove from mold and let cool completely.
For the glaze, mix all the ingredients together until smooth. Add more powdered sugar if needed.
Pour the prepared icing over the cupcakes. Decorate the muffins with confectionery sugar, berries, candied ginger, etc.