In a large bowl, whisk the flour, sugar, baking powder, and salt together.

Add the butter and mix with your hands until the mixture resembles cornmeal, or use a food processor to combine.

Add 1 cup of the cheese and all of the green onion.

Gently stir in the buttermilk and the milk starting by adding ¼ cup and adjusting as necessary. The dough should be sticky but not overly wet.

Cover the dough and let it sit for 30 minutes.

Move an oven rack to the top third of the oven and heat to 425 degrees.

Pour the dough onto a floured surface and roll it out until it is about ½ inch thick.

Fold the dough into thirds and roll it out again. Repeat this two more times for flaky layers.

Use a biscuit cutter or knife to divide the dough into about 12 biscuits.

Place the biscuits on a silicone mat or parchment-lined baking sheet and do not place in the oven until it reaches 425 degrees.

Bake the biscuits for 12 minutes. Then remove from the oven, brush with melted butter, and sprinkle the remaining cheese over the top.

Let cook for another 3 minutes until starting to brown. Turn on the broiler for about a minute to crisp the cheese.