Preheat the oven to 375°F (190°C). Lightly grease a 9-inch square baking dish or similar 2 to 2½-quart baking dish with softened butter, coating the bottom and sides.
In a large mixing bowl, combine the cherries, ¾ cup sugar, cornstarch, lemon juice, vanilla extract, almond extract (if using), and ¼ teaspoon salt. Toss gently until the cherries are evenly coated and no dry streaks of cornstarch remain.
Let the cherry mixture sit for 5 to 10 minutes so the sugar can start drawing out the juices. Pour the cherries and all their juices into the prepared baking dish and spread into an even layer.
For the topping, whisk together the flour, ⅓ cup sugar, baking powder, and ½ teaspoon salt in a medium bowl until well combined.
Add the cold butter cubes to the flour mixture. Use a pastry cutter, two knives, or your fingertips to cut the butter into the dry ingredients until the mixture looks like coarse crumbs with small pea-sized bits of butter throughout.
In a separate small bowl or liquid measuring cup, whisk together the milk (or buttermilk), egg, and 1 teaspoon vanilla until smooth.
Pour the milk mixture over the flour mixture. Stir gently with a spatula just until everything is combined and you no longer see dry flour. The batter should be thick but scoopable; if it seems too thick, add an extra tablespoon or two of milk, and if it feels too thin, sprinkle in a little more flour.
Drop the cobbler topping by spoonfuls over the cherry filling, covering most of the surface but leaving small gaps so the cherry juices can bubble up as it bakes.
Sprinkle the top of the batter with 1 to 2 tablespoons of coarse or granulated sugar for a light crunch and extra sweetness. Place the baking dish on a rimmed baking sheet to catch any bubbling juices.
Bake for 35 to 45 minutes, or until the topping is golden brown, the cherries are bubbling around the edges and through a few gaps in the topping, and a toothpick inserted into the center of the topping comes out without wet batter.
If the topping is browning too quickly before the filling is bubbling and thick, tent the dish loosely with foil and continue baking until the filling looks glossy and syrupy.
Remove the cobbler from the oven and place it on a cooling rack. Let it rest for 15 to 20 minutes so the juices can thicken slightly.
Serve the cherry cobbler warm, scooping it into bowls and adding vanilla ice cream or whipped cream on top, if desired.