Place stick of butter in the freezer while you prep the other ingredients. Shred cheddar cheese, chop ham and scallions (if using) and place back in fridge.
In a large bowl, whisk the flour, baking powder, sugar, and salt to combine.
Grate the partially frozen stick of butter with the big holes of your box grater into the dry ingredient bowl. Add the grated cheese, ham, and scallions (if using) and toss with a fork or by hand to combine.
In a small bowl, mix one egg and the milk together. Then slowly add to the rest of the ingredients, tossing with a fork or by hand to combine. Once it comes together in a shaggy ball (it should hold together if squeezed in your hand but not be overly moist) cover the dough in the bowl and place in the refrigerator for 20 minutes.
Preheat oven to 375℉
Remove the bowl from the refrigerator and transfer the dough onto a lightly floured surface. Gently pat the dough into a flat disc about 2 inches thick. Using a knife or bench scraper, cut the dough into quarters and stack the quarters on top of one another. Gently press down to smush them all back together again. Repeat this process 3-4 times. This creates laminated layers of butter throughout the dough, resulting in deliciously flaky scones. *If dough becomes sticky, you can lightly flour your hands so they don't stick when shaping the dough.
Cut the dough into 8 wedges. Place on a parchment-lined baking sheet. Whisk the second egg in a bowl and brush onto each scone.
Bake for 20 minutes or until the scones are a nice golden brown. Let cool slightly but not too long, scones are meant to be eaten warm and fresh!