Combine flour, soda, salt, and ginger in a large mixing bowl; set aside.
Bring molasses to a boil in a medium saucepan. Remove from heat; add butter, stirring until butter melts. Add molasses mixture to flour mixture, stirring well. Cover and refrigerate 1 hour.
Turn dough out onto a lightly floured surface. Roll dough into 1-inch balls; roll balls in sugar. Place 2 inches apart on ungreased baking sheets. Bake at 375° for 10 minutes. (Tops will crack.)
Note: Dough may be rolled to 1/8-inch thickness, and cut with a 2-inch cookie cutter. Sprinkle tops with sugar before baking.