Add 1/2 the butter to a heavy duty sauce pan and melt over medium heat. Swirl the butter and watch it closely until it starts to brown in the bottom. As soon as it is a caramel shade, remove from the heat and pour into a bowl. You don't want to let it burn as it gets bitter and doesn't taste good.
Allow the butter to cool for about 20 min. Add the other 4 oz of butter to a stand mixer and cream until light and fluffy. Add the browned butter, brown sugar, and vanilla and cream again.
In another bowl whisk together the flour, sugar, cornstarch, baking powder and salt.
Add the egg yolk to the mixer and blend well. Add the flour mixture and mix on low until barely combined. Remove the bowl and mix fully by hand so it doesn't overmix.
Wrap the dough in plastic wrap, it will be pretty soft, but will harden up in the fridge. Chill at least 1 hour, preferably a few hours.
Heat the oven to 325 and line a baking sheet with parchment.
Dust counter with flour and roll out the dough to 1/4 thick. Use cookie cutters or a pastry wheel to cut into shapes. Place on the cookie sheet and bake for 10-15 minutes until puffed and lightly golden. Do not let them get too dark. You can smash the scraps together into a ball and reroll to make another batch.
Cool on a rack until fully cooled then store in the freezer.