Prepare a grill for indirect heat. If using a charcoal grill, build the hot coals on one side only. If using a gas grill, heat one side only to medium-high heat.
Vigorously whisk together the eggs and 1/2 cup granulated sugar in a large bowl until pale and fluffy, about 2 minutes. Whisk in the cornmeal, flour and salt, smoothing out any lumps. Whisk in the milk and almond extract.
Add the butter to a 10- to 12-inch cast-iron skillet over direct heat. When the butter has melted, swirl it around to coat the bottom of the skillet. Right before you are ready to pour the batter into the pan, give the batter another whisk. (Cornmeal tends to sink to the bottom so re-whisking right before pouring it in is important.) Pour the batter into the cast-iron and cook until the batter begins to set, about 5 minutes. Every few minutes, using a rubber spatula, move some of the batter from the edges to the middle, like making scrambled eggs, to help it cook.
Remove the skillet from the grill and distribute the cherries evenly over the surface of the cake. Place the cast-iron over indirect heat, close the grill and bake until puffed and golden brown, about 30 minutes.
Remove the cake from the grill and immediately sprinkle it with the remaining teaspoon of granulated sugar. Allow to cool slightly before loosening and sliding it onto a plate. Slice and serve dusted with confectioners' sugar.
(Alternatively, you can begin to bake the cake over medium-high heat on a stovetop, then finish it in a 375 degrees F oven for 30 minutes.)