Myujth

Everybody knows that Santa employs elves to help him build his toys. Traditionally, they use hammers and other tools to build toy trains, dolls, horses, etc. As more children were asking for electronic toys for Christmas, the elves presumably started reading hammers in for soldering irons to build the circuit boards.

But nowadays, computers, video game consoles, phones, and other electronics can have processors with billions of transistors. As skilled as the elves are, I can’t see their skills of handcrafting toys to be able to create something that complex.

Assuming that Santa wants to keep his elves employed (rather than automating them out of existence), and that their only skill is in making toys (rather than factory building or whatever), How would Santa’s elves be able to build complex electronic toys?

I think you're giving the elves short shrift here. In particular, I think you may be focusing on the wrong elves.

Consider the svartálfar or "black elves" in Norse mythology, who were responsible for crafting a golden wig for Sif among other treasures - and are often conflated with the dwarfs, who have even more amazing feats discussed in this Literature.SE answer. Creatures capable of forging a self-duplicating gold ring, a boar with golden fur, a ship that can be folded up and put in one's pocket, and many unique weapons (including Mjölnir and Gungnir) clearly know secrets we've yet to plumb about the mysteries of the universe. I'm not going to bet that they can't handcraft modern electronics.

The most obvious course is to use a variation on the folding-ship technique: work on the circuits at an expanded size that's more amenable to handcrafting (keeping in mind their ability to work individual strands of golden hair), then shrink them down to their "proper" size. Or if that's not dramatic enough, maybe it's the workers who are folded down to tinker with individual circuits.

Sure, it's slow, but you can't put a price on proper (mythic) craftsmanship.

There are several foundries all around the world, producing integrated circuits for all our needs. These foundries run 24/7.

Once in a while some produced chip is defective, and get discarded from the production line.

Well, the trick is, the chip is not really defective. It's just a toll to Santa's production line. Then, once the chip is available, the elves can use their skills to assembly it into the desired product.

Santa not only have power to give things to kids who celebrate Christmas, but also the power to take things from ones who don't. Like those children who work at assembly lines in China or India.
Elves? Just a cover-up story.

The workers in chinese factories who assemble iPhones aren't very skilled either. Chips are printed by machines.

Elves are just the cheapest manual labor available, and Santa has just one upped every other third world country by having his assembly factory where no labor laws can reach.

Santa-type elves, Elfus SaintNickalus Arcticus, operate Santa's electronics manufacturing equipment building the printed circuit boards and microchips. Additional elves assemble these electronic components. Elves are excellent electronics manufacturers because of their small hands and mentorship training from other elves. They are excellent solderers and many are NASA certified. In fact, many elves worked on classified NASA projects because they were able to crawl inside the avionics compartments of the early space rockets which no human technicians were able to do. After the Cold War, the elves returned to Santa's toy production facility at the North Pole under the auspices of the United States Air Force during Operation Binderclip. This was all scrubbed from the official record to keep Santa's Workshop from becoming a primary nuclear target for anti-Christmas Soviet war planners. That's why I couldn't link any non-classified sources for you.

Think about it: why does NORAD track Santa every Christmas season? It's how NASA and the USAF honor him for his still-secret contributions to space science.

Much to the surprise of conspiracy theorists everywhere, the true role of the Illuminati is that of Santa's supply chain. When the department of defense budgets $600.00 for a hammer, it is really buying components for Santa's elf minions.

easy: Automated / computerized pick-and-place technology with board manufacturing on CnC routing, drilling, and soldering tables that have been computerized and fit into the assembly line. The elves run the robotic processes and troubleshoot issues on the assembly / production line, and refill the bins of components as they come in from IRT ordering vendors.