What breed do you cross Ameraucanas with to get Easter Eggers?
We don't breed our Easter Eggers with anything else, only Easter Eggers. Since you know Easter Eggers are not purebred birds, it's sort of a confusing thing to say, but keep in mind that the Easter Eggers were actually here first, before there were Araucana or Ameraucana breed standards at all. Let me explain:
The standards for breeding Araucanas were set up first, in kind of a backwards way. Normally, to get a new breed officially recognized, breeders get together and propose standards to the APA (American Poultry Association), and then there are certain requirements that must be fulfilled to get the APA to recognize the breed. But in the case of the Araucana, the APA proposed the standards themselves, rather than having breeders propose them. This happened in 1976; they proposed standards that preserved the look of the original Chilean ancestors to the the blue and green egg layers here in the US, the Easter Eggers. The Araucana standards included egg color (blue), but also rumplessness and tuftedness, among other things.
Unfortunately, this makes Araucanas very difficult to breed, since tuftedness is a fatal gene. About 25% of the chicks get two copies of that gene and die in the egg (that's where "fatal gene" comes in), 25% get no tuftedness, and only 50% get tufts. Of the chicks that are tufted, the tufts are rarely symmetrical, and there is additional mortality associated with chicks who have even one copy of the tufted gene, as they may have additional head/throat abnormalities. It's VERY VERY hard to breed birds when you lose so many in the egg, and when even the birds with the genes you want may not have the correct appearance. The rumplessness of the Araucana can even inhibit fertility if the feathers over the vent are long enough to interfere with mating. It's safe to say that most breeders agree: breeding Araucanas correctly is a real pain in the neck, even when you are successful!
In 1984, breeders got together and proposed standards for a new colored egg layer, the Ameraucana, to the APA in the regular way. This was their idea of an "improved" Araucana. Breeders made the standards for the Ameraucana much more reasonable to achieve, on par with other APA breeds. They must lay blue eggs, have tails, and beards rather than tufts (beards are not fatal). There are other specific requirements of plumage color, comb, body conformation and so on, but they differ from the Araucana in having tails and in their beardedness (rather than tuftedness).
In the meantime, hatcheries have continued to offer the blue/green egg layers that are not bred to any standard: the Easter Eggers. The Easter Eggers were around first, and were used to develop both other breeds here in the US. The EEs originated from various breeds of blue/green layers brought originally from Chile, including the Quetro and the Collonca. They are not Ameraucanas or Araucanas cross bred with other birds. They are simply birds with the colored egg gene that do not fit the standards the APA approved for the Araucana, nor the standards that the breeders proposed (and got approved) for the Ameraucana.