In a medium bowl toss the hulled and halved strawberries with 1/2 cup sugar, 1 tablespoon lemon juice, 1 tablespoon cornstarch, and 1/4 teaspoon salt; let sit 10–15 minutes at room temperature until juices form.

Preheat oven to 425°F. In a separate bowl whisk together 2 cups flour, 2 tablespoons sugar, 1 tablespoon baking powder, 1/2 teaspoon baking soda, and 1/2 teaspoon salt. Grate or cut 1/2 cup cold butter into the flour and toss until the mixture resembles coarse crumbs with pea-size pieces. Stir in 1 cup cold buttermilk until dough just comes together; it should be slightly sticky.

Lightly butter a 9×13-inch baking dish and pour the macerated strawberries and any juices into it, spreading into an even layer. Drop the biscuit dough by spoonfuls over the berries, leaving small gaps for steam to escape. Brush the dough lightly with 2 tablespoons melted butter and sprinkle with 2 tablespoons coarse sugar if using. Bake at 425°F for 12 minutes, then reduce oven temperature to 375°F and continue baking 18–22 minutes until the topping is golden and a toothpick inserted into the biscuit comes out with moist crumbs but no raw dough. Remove and let rest 15 minutes before serving.

Spoon warm cobbler into bowls and serve with vanilla ice cream or whipped cream if desired.