Preheat oven to 400°.
Combine 3/4 cup granulated sugar, brown sugar, and butter in a medium bowl; beat with a mixer at medium speed until light and fluffy. Beat in vanilla and egg.
Lightly spoon flour into dry measuring cups; level with a knife. Combine flour, baking powder, 1/2 teaspoon cinnamon, and salt, stirring well with a whisk. Add flour mixture to butter mixture; beat just until combined. Shape dough into 30 balls.
Combine 1/3 cup granulated sugar and 1 1/2 teaspoons cinnamon in a small shallow dish. Roll balls in sugar mixture, and place 2 inches apart on baking sheets coated with cooking spray. Bake at 400° for 8 minutes or until tops crack. Cool on pans 1 minute. Remove from pans; cool on a wire rack.