Place first 3 ingredients (through oil) and 2/3 cup sugar in a large bowl; beat with a mixer at medium speed until well blended. Add milk, vanilla, and egg. Beat until blended.
Weigh or lightly spoon flour into dry measuring cups; level with a knife. Combine flour, baking powder, and salt; gradually add to sugar mixture, beating until well blended. Cover and chill 30 minutes.
Preheat oven to 350°.
Place 1/3 cup sugar in a small bowl. Shape dough into 36 (1-inch) balls. Roll balls in sugar, and place 1 1/2 inches apart on large baking sheets coated with cooking spray. Flatten cookies slightly with bottom of a glass.
Bake at 350° for 9 minutes or until set in center. Cool on pan 2 minutes. Remove from pan; cool completely on a wire rack.