Preheat your oven to 350°F (175°C) and place an oven rack in the middle position.

Line a baking sheet with aluminum foil.

In a 10- to 11-inch ovenproof skillet, combine 4 tablespoons of unsalted butter, ⅓ cup of dark brown sugar, 2 teaspoons of balsamic vinegar, and 1/8 teaspoon of salt over medium heat.

Stir until the butter melts and the sugar dissolves.

Increase the heat to high and add the 4 cups of pitted cherries. Bring to a boil for about 30 seconds, then remove from heat.

In a medium bowl, whisk together 1⅓ cups of cake flour, ½ cup of cornmeal, 1½ teaspoons of baking powder, ¼ teaspoon of baking soda, and ½ teaspoon of salt. Set aside.

In a stand mixer, beat ½ cup of softened unsalted butter and ¾ cup of granulated sugar on medium-high speed until light and fluffy (about 3 to 4 minutes).

Add the eggs one at a time, blending well after each addition, then add ¾ teaspoon of vanilla extract and ¼ teaspoon of almond extract.

Gradually incorporate one-third of the flour mixture, then half of the buttermilk, and continue alternating until everything is mixed in.

Spoon the batter evenly over the caramelized cherries in the skillet.

Bake in the preheated oven for approximately 45 minutes, or until the top is set and golden brown.

Allow the cake to cool in the skillet for about 15 minutes, then invert onto a platter.

Serve warm or at room temperature, optionally with vanilla ice cream or sweetened whipped cream.