Heat oven to 400°F and line a baking sheet with parchment paper or a silicone liner.
>Melt ½ tablespoon butter in a small skillet over medium heat. When it foams, add apple and cook, stirring, for about 1 minute. Sprinkle 1 tablespoon sugar over apples and stir to coat. Continue to cook, stirring, for another 3 to 4 minutes, until the apples have softened and begun to caramelize. Remove from heat and set aside.
>Whisk remaining 2 tablespoons sugar together with flour, cornmeal, baking powder, baking soda, and salt in a large bowl. Add sage, cheese, and remaining 8 tablespoons butter and rub into mixture with your fingertips until mixture is shaggy and pebbly.
>Whisk together egg, buttermilk, cream, and vinegar in a small bowl and pour over dry ingredients. Stir gently with a fork until dough comes together. Knead in the bowl or turn dough over itself a few times with a rubber spatula.
>Transfer to a lightly floured work surface (dough will be sticky) and pat into a ½-inch-thick square. Cut into 12 even pieces and transfer to prepared baking sheet. Bake for about 20 minutes, until scones are browned on top with bits of lacy-crisp melted cheese around the edges.