On Facebook, Friend-of-The-Food-Geek Mary asks:
Here's a query for you - it's to do with baking with melted vs. softened butter - why does it matter? http://driedfigsandwoodenspool
With many cookies and cakes, the traditional advice is to cream the sugar into the butter. Creaming, in this context, means to beat the sugar into softened, but still solid, butter until it is thoroughly integrated. This causes little bubbles to appear in the butter which, when baked, turn into slightly larger, and very evenly distributed, bubbles throughout your confection.
This is not the only way to make cookies or cakes, however. My favorite chocolate cake is a Nigella Lawson Chocolate Guinness Cake, which calls for melting the butter instead of creaming it. This is the 'dissolved sugar method' with cake making, though I don't know of an equivalent method in cookie making. So melting the butter is not unheard-of, it's just not as popular as creaming.
When you melt the butter, you're making a trade: instead of a bit of rise and a particular texture, you want a cookie that will be less chewey. You are coating the flour with melted fat, which keeps water from mixing with the flour (after all, water and oil don't mix without… encouragement). Less gluten means the cookies will be more tender.
Also, the water from the butter and the eggs, which is the only water in the recipe which led to this question, will be more likely to stick with the sugar instead of the flour, making a cookie that's a bit more moist.
In the dissolved sugar method of cake making, having the sugar tie up the water is a much more explicit goal than it is with cookies. It's a slightly tricky method to pull off, though, because…
In the dissolved sugar method, you dissolve your sugar in your liquid, melt the butter into it, add flavorings, mix the dry ingredients together, and add the dry ingredients to the wet ingredients. The last bit is the tricky bit, because if your liquid is warm enough to dissolve granulated sugar, then it's probably going to cause the flour to clump together as if you were making gravy badly.
To avoid the clumping, probably the most effective way is to sift your flour into the liquids slowly. Alternately, you can reserve a portion of your liquid, don't heat it up or mix anything into it, and combine it cold with your flour. It's unlikely you'll have enough liquid to do this effectively, but if you hate sifting, you can give it a go. Now I'm wondering just what would happen to a cake if you made a roux out of the butter and flour and treated the rest of the cake with the normal dissolved sugar methodology.
[Note to self: try this. Alternate toasting the flour or not toasting it. Expect texture to not work out.]
[Note to readers: if you try this, let me know how it goes.]
Here's another thought: as you are already melting the butter, would there be extra flavor if you went ahead and turned it into brown butter, or does the cookie baking process already do that?
Gluten formation, texture, moisture, and rise are the primary ways the state of butter will affect your baked goods. Though, as you can tell, there are many other ways things could change, and I look forward to which new techniques will be the most rewarding.