Preheat oven to 400 degrees.
In your mixer combine flour, sugar, baking powder, salt, cinnamon, nutmeg, and ginger. Cut the cold butter into small pieces and add to the dry mixture. Mix together until the butter is broken into small little pieces. It will take time so just be patient and it will break down!
Mix in the milk or cream, vanilla, and shredded carrots until moistened. Turn out the dough onto a floured surface and divide dough in half and by hand form both sections into circles. You want the dough about an inch thick. Then cut each circle into 8 pieces like a pie with a dough cutter.
Place 2 inches apart on a cookie sheet. Bake for about 17 minutes or until golden brown. Cool slightly and drizzle with glaze.
Cream Cheese Glaze:
In a small bowl smash the cream cheese with a spoon and then add the butter and mix till smooth. Add the milk and powdered sugar and mix till smooth and the right consistency to drizzle. Add more milk if needed.