Lightly spoon flour into dry measuring cups; level with a knife. Combine flour, baking soda, and next 5 ingredients in a medium bowl.
Beat butter with a mixer at medium speed until creamy; gradually add 1 cup brown sugar, beating well. Add egg and molasses; beat well. Add flour mixture; beat until smooth. (Dough will be slightly crumbly.)
Shape dough into 1-inch balls. Roll balls in 2 1/2 tablespoons sugar. Place balls 1 1/2 inches apart on baking sheets coated with cooking spray. Bake at 350° for 8 minutes. Cool 2 minutes on pans. Remove from pans; cool completely on wire racks.