1/4 cup unsalted butter, softened
1 cup plus 1/3 cup sugar, divided
1 large egg, beaten
1/4 cup molasses
2 cups all-purpose flour
2 teaspoons baking soda
1 teaspoon ground cinnamon
1/2 teaspoon salt
1/4 teaspoon ground cloves
1/8 teaspoon ground ginger
1/3 cup crystallized ginger, finely chopped