Shortcakes come in many varieties, from rich sponge cake-like versions to those resembling biscuits. This method yields shortcakes with a sturdy crumb, similar to that of a corn muffin. They're delicious served warm straight from the oven or for breakfast the next morning.
Preheat the oven to 425 degrees and line a baking sheet with parchment paper.
Put the flour, cornmeal, sugar, baking powder, and salt in the bowl of a food processor and pulse until combined. Add the butter and pulse until the mixture resembles breadcrumbs. Add the milk and vanilla extract while continuing to pulse, just until the mixture comes together and forms a thick batter.
Drop the batter by the heaping spoonful onto the baking sheet to form 8 shortcakes. Bake until golden and cooked through, about 15 minutes. Remove from the oven and set aside to let cool.
Meanwhile, put the cherries, wine, and nutmeg into a small pot and bring to a boil. Reduce the heat to medium-low and simmer until the liquid is thickened and the cherries are very tender, about 30 minutes. Remove from the heat and set aside.
To serve, halve the shortcakes and arrange on individual plates. Spoon the cherry compote over the bottom half of each shortcake then arrange the remaining halves on top. Serve with dollops of whipped cream, if you like.