Do you have a specific concern about breeding EE’s to each other? If so, that might help us answer better. There are several different ways to take that. It might help a bit to know something about the genetic background of your birds. Them being EE really does not tell us anything about their genetic background. They could be anything from pureblooded Ameraucana or Araucana that don’t meet breed standards to jumbled mixes of several breeds.
There can be some concerns with breeding any chickens, purebred or mutts, to close relatives. We do that all the time. That’s how breeds were developed and how grand champions at shows are bred, but if there are defective recessive genes present, they can show up. If yours are from a hatchery, they are probably not all that closely related. We can talk a whole lot more about this if this is your concern. There are different techniques to handle this.
The Araucana and Ameraucana breeds were developed from blue egg laying birds originally from Chile. Your EE’s may have Araucana or Ameraucana in their background or they may not. The Araucana have a fatal recessive gene, related to the gene that makes them rumpless. If that recessive gene pairs up with another recessive gene, that chick will die before it hatches. That fatal gene has been bred out of Ameraucana. Most EE’s don’t have it. If your EE’s have tails, yours probably don’t have it. You can Google photos of Araucana to see what I mean by rumples or tailless. I hate to mention this because some people will freak out when they don’t need to, but this is a possibility if your birds are rumpless when mature.
The blue egg gene is dominant. If just one of the pair of genes that determine basic egg shell color is the blue egg gene, the hen will lay a blue or green egg. The green comes from brown being deposited over the base blue. Since it is dominant, you don’t know if both of that gene pair are blue egg genes or if she is split for that gene (one blue and one white) even if she is laying blue or green eggs. Since EE roosters don’t lay eggs, you don’t really know if they have any copies of the blue egg gene. One of the genetic experts on here said the blue egg gene follows the pea comb gene about 97% of the time, so if they have a pea comb it is an indication they might have at least one copy of the blue egg gene, but it is not a guarantee.
If the hen is split for the blue egg gene (one blue and one white egg gene) and you breed her to a rooster that does not have the blue egg gene, half her offspring will have the blue egg gene and half won’t. If you breed that split hen to a rooster that is split for the blue egg gene, about ¾ of their offspring will have the blue egg gene. If either is pure for the blue egg gene, then all their offspring will have at least one copy of that gene. So if you want blue or green eggs, it is a good idea to breed EE’s to EE’s.
Those are the main things I can think of that might have been your concern. If you have any other specific concerns or need clarification, please be specific.
I strongly encourage you to play with that genetic calculator. It can be addicting, but it is a lot of fun for me and you can learn a lot. But be prepared for some surprises in what you hatch for a couple of different reasons. One is that the genetic odds are just odds. You never know how those genetics are going to go together with any specific chick. The odds really don’t mean anything unless you hatch a whole lot of chickens. For example, I once hatched four chicks. Two of the four were red barred. The next hatch with the same parents, I hatched 17 chicks. None of them were red barred. What you get with any individual chick is just a roll of the dice.
The other thing is that chicken genetics can get pretty complicated. You not only have dominant and recessive genes, you have partially dominant or shared dominant genes. Just one copy of one gene showing up can really change the appearance of the bird. There are so many “if’s” involved it is hard to come up with a simple specific example but I’ll try the blue gene. How it shows up depends in what other genes are present. If it is paired with black, two copies of the blue gene gives you what is called splash. Splash is a white and black bird. If only one copy of the blue gene is present with black, you get a blue bird. If no copies of blue are there, you get a black bird. If blue is paired with something other than black, you may get a chicken that is only partially blue, like maybe just a blue tail. This is only one example. It is possible to cross white chickens and get black chicks. What you get just depends on what genes are present and some of those can be hidden. Be prepared for surprises. Some of those surprises can be very attractive.
I know this is very long. Hopefully you get something useful out of it. The short simple answers to your questions are that there is probably nothing wrong with breeding EE’s to EE’s and it may even be desirable if you want blue or green eggs and that you should try the genetic calculator but be prepared for surprises.
Good luck!!!
Hens go broody when you don’t want them to… and won’t go broody when you do. 
