Preheat to 350°F (175°C). Line a 9x13-inch pan with parchment or grease well.
Whisk melted butter, brown sugar, and granulated sugar in a large bowl until smooth. Beat in eggs and vanilla.
In another bowl, whisk flour, baking powder, cinnamon, cream of tartar, and salt.
Stir dry ingredients into the wet mixture just until no dry spots remain—don’t overmix.
Spread batter in the pan. Bake for 25–28 minutes, until edges are golden and center is just set. Cool completely.
Beat butter until creamy. Gradually add powdered sugar, cinnamon, and vanilla. Add milk 1 tbsp at a time until smooth and spreadable.
Spread frosting on cooled bars. Optional: Sprinkle with cinnamon sugar. Slice and enjoy!