Preheat the oven to 425° F.
In a large mixing bowl whisk together the flour, the granulated sugar, baking powder and salt.
Slice the cold butter into small pieces. Add the butter to the flour mixture and use a pastry blender to cut it into the dry ingredients. If any large pieces remain, use your fingers to squeeze and flatten them.
Add in the half and half and use a spoon to toss and combine the mixture.
Lay a long piece of parchment paper over your work surface and dust with flour - or, lay out a large Silpat baking mat. Turn out the contents of the bowl.
Sprinkle the top of the dough with a bit more flour and knead by hand for 2 or 3 minutes until it has just come together into a smooth dough (add a sprinkle more flour to the work surface or dough to keep it from getting too sticky.)
With a floured rolling pin, roll the dough out into a rectangle roughly 10 inches by 15 inches, and ½ inch thick. Transfer the paper or Silpat with the dough to a large baking sheet.
Bake the shortcake in the preheated oven for 8-10 minutes, until the cake is puffed and just turning a light brown. Place the pan on a cooling rack and allow it to cool completely.
Place the bowl and whisk attachment of your stand mixer into the freezer.