Place flour in a medium bowl and add cold butter cubes. Use your fingers to quickly break the butter down into the flour. Some of the butter bits will be the size of oats, some the size of small peas. Stir in the granulated sugar.
Create a well in the center of the butter and flour mixture and add 2/3 cup buttermilk. Stir the mixture together until it is well moistened and holds together well.
Biscuit dough should be soft and moist; add the remaining buttermilk as needed.
Generously dust a clear work surface with flour and spoon dough onto the floured surface.
Use your hands to gather it into a ball and gently pat it into a small rectangle.
Gently roll the dough into a rectangle 1/2-inch thick, about 7-inches x 10-inches.
Arrange cooled apples in a single layer over half of the rolled out biscuit dough. Fold the bare side of the dough over the apples and gently press the edges to seal in the apples. Use the palms of your hand to pat the dough into a 6 x 8-inch rectangle if the edges are looking a bit rounded.
Use a sharp knife to slice the dough into 12 squares. Use a spatula to place each biscuit onto the prepared baking sheet, about 2-inches apart.
In a small bowl, whisk together sugar for topping, cinnamon, and salt.
Brush each biscuit top with beaten egg and sprinkle generously with the cinnamon sugar mixture.
Bake for 12 to 14 minutes until the biscuits are risen and golden brown.
Remove from the oven and serve warm or cool completely before storing. Biscuits are best enjoyed within two days of baking.