Baking Pastry – What Is the Difference Between Using Hot Water and Cold Water in Pastry Making?

Basically, when recipies call for softened butter, they use the creaming method; the sugar and butter are mixed together in such a way that the sugar cuts little air bubbles into the butter. These little bubbles can add some extra puff to the cookies.

If you melt the butter first, not only do you not have those air bubbles, but there's water in butter, so you'll end up getting some gluten development when you mix in the flour and make a chewy cookie ... but more importatly, without the fat being (near) solid, the cookie will slump a lot more, and spread out before it cooks (assuming you haven't otherwise adjusted the recipe to compensate).

There are cookie recipes that call for melted butter; compare the three recipies from the "Three Chips for Sister Martha" episode of Good Eats; the "chewy" cookie uses melted butter.

Milk contains several components, most notably fat, sugar, and protein. These all add to the browning effect when cooked at high temperature (proteins cooked together with either sugars or fats undergo the "Maillard reaction"). The browned bits do have significant extra flavor, but it does not taste like milk.

Egg white, by itself, is pure protein. It is typically used in pre-baked ("blind baked") pie shells because the dense protein creates a water-resistant coating when it cooks, so that the crust won't get too soggy when a liquid filling is added later on. Quiche is a great example of this application. Like milk, the egg white will add no flavor of its own, just the flavor associated with browning. Egg white is also used in low-cholesterol cooking.

Egg whites will brown some, but not as much as milk unless the pastry itself provides extra fats and sugars for the proteins to react with. Egg wash -- beaten whole eggs, usually mixed with a little water -- is more typically used to get pastries to brown.