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The color genetics on EEs are so messed up that you can't really predict them. That's why they say they don't "breed true". However, you can guess. There are a few threads on here that deal extensively with color genetics - but they get really in-depth. I am still trying to learn about them. There is a Chicken Calculator you can play with (
http://kippenjungle.nl/kruising.html) but you really need to know what the genetics are to start in your bird with to know what you will get. Its still fun to play with though.
By BR do you mean a Barred Rock rooster? I never liked my feedstore Barred Rocks -they were always mean. If yours is a nice boy you can cross them. I think if you cross them all the chicks will be black and white incomplete barred - since Black is dominant over the wild-type coloring. At least, that would be my guess.
Since Barred Rocks do not carry the blue egg gene, and since there is a chance your girls are not homozygous for blue eggs (O/O) you may end up with some girls that lay a brown egg. I have one EE that lays a white egg - so they can loose it, especially if outcrossed enough times.