In a 9 or 10-inch oven proof skillet over medium heat, combine 1/4 cup butter, brown sugar and balsamic vinegar, stirring until butter melts and sugar dissolves. Increase the heat to high. Add cherries. Bring to a boil, then remove from heat. Set aside. (**Note: If no oven-proof skillet is available you may complete the cherry mixture cooking step in a saucepan or skillet and then transfer to a greased 9-inch cake pan for baking.)
In a medium bowl, combine cornmeal, flour, baking powder and salt. In a large bowl, cream 1/2 cup of butter and sugar in a large bowl until light and fluffy. Add egg yolks and vanilla and beat until well combined. Add flour mixture alternately with milk in several additions, beating just until blended. Set aside.
In another medium sized bowl, beat egg whites with clean, dry beaters until light and foamy. Add cream of tartar and beat until stiff peaks form. Using a rubber spatula, slowly and gently fold in whipped egg whites into cornmeal batter in several additions. Pour and spread batter evenly over the top of the cherries in the skillet or baking pan.
Bake cake in a preheated 350˚F oven for 40-45 minutes, or until golden brown and a tester inserted in middle of cake comes out clean. Cool in skillet for 5 minutes. Run a knife around edge of skillet to loosen, then invert the cake onto a plate or platter - leave skillet or baking pan to rest atop cake for a few minutes, then remove. Scrape any remaining cherries or brown sugar glaze that may have stuck to the bottom of the skillet onto the cake. Let the cake cool for 45 minutes (20 minutes if you'd like a slice while it's warm.)