Position rack in center of oven and preheat to 350°F. Grease a 9- by 13-inch baking pan with butter (or spray with cooking spray); set aside.
In a medium bowl, whisk together flour, baking powder, cream of tartar, and salt. In a large bowl, use an electric mixer to stir butter until creamy. Blend in sugar and brown sugar and beat on medium-high speed for 3 minutes or until light and fluffy. Mix in the eggs, one at a time, and vanilla, and blend until smooth.
Mix in the flour mixture until well combined. Spread in an even layer in the prepared pan. In a small bowl, mix the sugar and cinnamon. Sprinkle evenly over the top of the batter.
Bake for 25 to 30 minutes or until a toothpick inserted in the center comes out clean. Cool in the pan on a wire rack. Cut into 20 bars.