Preheat your oven to 450F. In a large bowl, mix the flour, 2 tablespoons of sugar, salt, and baking powder. Cut the cold butter into the flour mixture with a pastry cutter (you can do this in a food processor as well, but I prefer by hand). Keep "cutting" the butter into the flour until the whole mixture looks like coarse crumbs.
In a small bowl, lightly beat the whole egg and add the milk and vanilla extract to the bowl. Stir.
Add the wet mixture to the dry mixture all at once and stir until everything is moistened. This is tricky, but you don't want to over mix (tough shortcakes), but do your best. There will be some flour pockets left.
Dump the dough out onto a well floured surface and kneed for 10-12 pushes. Just enough to bring it together. Shape and then flatten the dough using the palms of your hands to about 1/2-3/4 inch thick circle.
Using a lightly floured biscuit cutter or 3 inch across drinking glass, cut out several circles and transfer to a lined baking tray. You want to have 6-7 rounds. After the first cut, gently bring the dough together and flatten again, to cut batch #2.
Once the shortcakes have been cut and transferred to the baking sheet, take a small bowl and whisk together the egg yolk and half & half. Brush the tops of the shortcakes with the glaze.
Bake for 10-15 minutes, or until perfectly golden.
Transfer to a wire rack to cool.