Preheat the oven to 425°F.
Line a baking sheet with parchment paper.
In a large mixing bowl, combine the all-purpose flour, ground cornmeal, granulated sugar, salt, baking powder, and baking soda.
Add the Italian seasoning, if preparing herb biscuits.
Stir the dry ingredients until evenly combined.
Add the cold unsalted butter to the dry ingredients.
Using a pastry cutter or the backs of two forks, cut the butter into the flour mixture until pea-sized pieces of butter remain throughout.
Add the shredded cheddar cheese to the bowl.
Stir until the cheese is evenly distributed.
Pour the milk and white vinegar into the bowl.
Using a rubber spatula, stir the mixture just until a shaggy dough forms.
Do not overmix the dough.
Transfer the dough to a lightly floured surface.
Gently bring the dough together with your hands.
Pat the dough into a 1-inch-thick rectangle.
Cut the dough into 3 equal rectangles.
Stack the rectangles on top of one another.
Gently press or roll the stacked dough into another 1-inch-thick rectangle.
Repeat the cutting and stacking process two more times.
After the final stacking process, roll or pat the dough to 1/2 to 2/3 inch thick.
Flour a 1 1/2-inch round biscuit cutter.
Press the cutter straight down into the dough to cut biscuit rounds.
Do not twist the cutter, as twisting may seal the edges and limit rising.
Re-flour the cutter as needed and continue cutting biscuits.
Gently gather any remaining dough scraps and form them back together.
Cut additional biscuit rounds until all dough has been used.
Arrange the biscuits about 1/4 inch apart on the prepared baking sheet.
Bake for approximately 12 minutes, or until the biscuits have risen and the tops are golden.
Remove the biscuits from the oven.
Brush the warm biscuits with the melted butter, if desired.
Allow the biscuits to cool slightly before serving.
Serve warm.