Grate or dice the cold butter. Then, place the butter in the freezer until step 5.
Next, sift the flour and baking powder to a large bowl. Then, add the sugar and salt. Whisk the ingredients together until combined.
Next, remove the butter from the freezer and add the butter pieces to the flour mixture. Use a pastry cutter or fork to cut the butter into the flour until the mixture resembles coarse, pea-sized crumbs. Alternatively, a food processor will work as well.
Next, push some of the flour mixture to the edges of the bowl to resemble a well. Next, gradually add the buttermilk to the center of the well. Then, add the vanilla extract. Next, stir the mixture gently until the dough comes together. Do not overwork the dough. The dough should look crumbly, yet moistened.
Dump the dough into a lightly floured surface. With floured hands, bring the dough together by kneading it a few times. Be careful not to overwork the dough. With your hands or a rolling pin, pat dough into a rectangle. Next, cut the dough into three equal rectangles with a floured knife. Stack the rectangles on top of each other to form 3 layers (alternatively, you can fold the dough letter style to form 3 layers). Roll or pat out the layered dough into another rectangle and repeat the process two more times. Then, pat or roll the dough out to about 1/2-inch to 3/4-inch thickness.
Next, use a 2.5-3.0 inch biscuit cutter or the rim of a glass to cut out biscuits. When cutting the dough, be sure not to twist the cutter, as twisting the cutter will prevent the dough from rising. You can also use a sharp knife to cut the biscuits into squares if you do not want to use a biscuit cutter. Once the biscuits are cut, place the biscuits in the prepared baking sheet about 2 inches apart.
Brush the tops of the biscuits with the egg wash and bake the biscuits in the preheated oven for 15-18 minutes, or until the biscuits are golden brown on top.
Once done, remove the biscuits and brush the biscuits with melted butter.