In large bowl, whisk together the all purpose flour, cornmeal, baking powder, sugar, salt and cayenne pepper. Add the cubed, cold butter. Using pastry blender, cut in butter until crumbly, with about pea-sized pieces of butter. Add the green onion and shredded cheese and stir to coat with flour. Pour about half of the milk into the bowl and stir in. Begin adding the remaining milk, adding it a bit at a time and stirring between additions, adding only as much milk as is needed until the dough comes together in a moist, but not sticky dough. There should be any dry flour visible in the bowl, especially on the bottom. You may not need all the milk (or you may need a splash more). Just use what you need.

Turn the dough out onto floured surface and with lightly floured hands, knead gently a couple of time, then pat into a round about 1-inch thick.

Line a baking sheet with parchment paper and sprinkle with a little cornmeal. Transfer the round of dough onto the parchment. Using a sharp knife, cut the round into 8 equal-sized wedges, then use a spatula to move the wedges apart, so there is some space between each wedge. Brush the top of the biscuits with buttermilk or milk and sprinkle with a bit of coarse salt, if using. Bake for 18 to 20 minutes or until golden.