Cream the butter and brown sugar in a large mixing bowl with mixer on high speed until light and fluffy, about 1 minute. With mixer on medium speed, beat in the egg and molasses, then increase the speed to high and beat about 1 minute longer, until the mixture no longer looks curdled. Scrape the sides with a rubber spatula several times while mixing.
Mix in the flour mixture on low speed. The batter will be rather stiff. Place some granulated sugar on a small plate or saucer. Use a 1/4-cup ice cream scoop or a measuring cup to form 1/4-cup portions of dough. (Spray the cup or scoop with the optional non-stick vegetable spray to make it easier to release the dough.) Transfer the dough to your hands and roll each portion into a rough ball, then roll each ball into the sugar. Place six sugared balls on each baking sheet, spacing them evenly, because they will spread during baking. Dampen your fingers with water and press down lightly on each cookie to flatten it a little and dampen the top. Refrigerate one filled baking sheet while the other bakes. Bake for 12 minutes, or until the cookies have spread and are firm to the touch. Rotate the sheet 180 degrees halfway through the baking time. Remove from the oven and let the cookies cool on the baking sheet. Note: This dough can be frozen for slice-and-bake cookies. Just roll into a log 2 1/2 inches thick. Wrap in plastic wrap and then in foil. Can be stored in the freezer up to 6 months.