Place oven rack in the center of oven. Preheat oven to 350˚F.

In a 10 or 11-inch oven-proof skillet with at least 2-inch tall sides, stir together ¼ cup of the butter with the brown sugar and balsamic vinegar. Place over medium heat, and stir for about 2 minutes, until the butter melts and the sugar dissolves. Increase the heat to high, then add the cherries and bring to a boil. Remove from heat.

In a medium bowl, whisk together the flour, cornmeal, baking powder, and salt until combined. Set aside.

Place ½ cup of butter in a large bowl, and beat with an electric mixer. Add the sugar, and continue to beat for 3 minutes, until fluffy and pale. Add the egg yolks and vanilla, and beat to combine. Add the flour mixture alternately with the milk, in 2 additions each, beating just until blended, occasionally scraping down the sides of the bowl. Set aside.

Place the egg whites in a medium bowl, and use clean (and dry) beaters to beat until foamy. Sprinkle in the cream of tartar and beat until egg whites are stiff but not dry. Use a rubber spatula to fold ¼ of the egg whites into the batter. In three additions, fold in the remaining egg whites. The resulting batter will be thick. Spoon the batter over the cherries in the skillet, and spread evenly to cover.

Bake for 45 minutes, until golden brown on top and a tester comes out clean. Allow to cool in the skillet on a wire rack for 5 minutes. Run a sharp knife or spatula around the edges of the cake to loosen. Place a large serving platter on top of the skillet, then (using oven mitts) firmly hold the platter and skillet together and invert. Let the skillet sit on top of the platter for 5 minutes before removing. Allow the cake to cool at least 45 minutes before slicing into wedges and serving. Delicious slightly warm, or at room temperature.