Preheat the oven to 325 degrees.
Put ½ cup of granulated sugar, the brown sugar, and the butter in the bowl of an electric mixer. With the paddle attachment, cream the butter on medium speed for 2 minutes, until the mixture is light and fluffy. Continuing to mix, beat in the egg and then the molasses. On low speed, add the dry ingredients and mix until incorporated. Refrigerate the dough for 30 minutes.
Roll the dough into ¾-inch balls and roll them in the remaining ½ cup of sugar. Line a baking sheet with parchment paper. Put the cookies 2 or 3 inches apart on the baking sheet. Flatten them slightly with 2 fingers.
Bake the cookies for about 12 minutes, until golden brown and set around the edges but still soft inside. Let them cool for 5 minutes and then remove them from the baking sheet.