What impact does the order of assembly have when making cookies?

Generally with baking you mix all the wet ingredients, then all the dry, then incorporate the latter into the former. This prevents clumping and helps make sure everything is mixed uniformly.

In some recipes, adding the eggs (often un par un, or one by one) also contributes (via the yolk's supply of lecithin) to emulsifying e.g. butter and milk together.

The best way to find out, of course, is to experiment. Next time you're making these cookies, make a double batch. Do one according to the recipe, and the other your way. Honestly with cookies I doubt you'll see much difference; they're basically foolproof (I have, when in a hurry, made chocolate chip cookies by dumping everything in the mixer, whacking it about with the paddle attachment, and then folding in the actual chips. Worked fine, basically). When it comes to baking things that are more finicky--cakes etc--I would follow the recipe directions.

First, fat & sugar are part of the wet ingredients.

Given that, I do it different than daniel suggests. I always add the wet to the dry.

Adding the wet to the dry tends to be less messy, and allows for easier mixing when you start. It's less messy because you're not pouring powdery dry ingredients. It mixes somewhat easier at the start because you're pushing the wet into the dry instead of pulling it up through the dry. This means you're also less likely to flip a big cloud of dry ingredients across your kitchen.

This technique is explained by Alton Brown in his book I'm Just Here for More Food: Food + Mixing + Heat = Baking.

See Also:

• A chowhound thread which contains supporters for both methods, and in which some claim that it wet-to-dry leads to less clumping.

I think the key in this case is making sure that you've thoroughly incorporated everything. Since (wheat) flour has gluten, the more you mix it while wet, the tougher it can become, hence mixing the egg thoroughly with the butter and sugar first. Is it going to cause disasterous results? Unlikely, unless things aren't mixed well.

There was a mention on Serious Eats that mixing baking powder with the sugar before creaming gives you a dough that you can wait longer before baking (as the butter coats the baking powder keeping from reacting with the liquids until it's baked.)

I would suspect that mixing the flour into the creamed butter before adding the eggs or other liquid could do the same thing to a lesser degree. It could also coat some of the flour, giving you a more tender cookie vs. the chewiness from developing the gluten.