Place flour, cornmeal, sugar, baking powder, salt, baking soda and butter in food processor bowl with cutting blade. Pulse the food processor until mixture resembles coarse meal.
Transfer mixture to large mixing bowl. Fold in buttermilk, cheese and scallions. Knead together very gently until just combined.
Roll out on floured surface to about 3/4” thick and cut into 2-inch round biscuits.