Mix flour, ginger, cinnamon, baking soda, nutmeg and salt in large bowl. Beat butter and brown sugar in large bowl with electric mixer on medium speed until light and fluffy. Add molasses and egg; beat well. Gradually beat in flour mixture on low speed until well mixed.
Preheat oven to 350°F. Shape dough into 1-inch balls. Roll in granulated sugar. Place 2 inches apart on ungreased baking sheets. These can be refrigerated and baked the next day.
Bake 8 to 10 minutes or until edges of cookies just begin to brown. As soon as cookie come out of the oven, make a “thumbprint” in the cookie using the back of a measuring spoon or end of a wooden spoon (or your thumb… but they are hot!). Cool 2 minutes on the cookie sheet before removing to a cooling rack.
To make glaze, combine butter and white chocolate in a microwave safe bowl. Cook on high, stirring every 15 seconds until smooth. Gradually beat in powdered sugar and milk until icing is of a drizzling consistency. Fill thumbprints. Put in the frig or a cool place so the glaze can set.