Nope, the orpington is not annoying the EE, this behavior is pretty common, it is usually due to the personality of the bully. When hens are laying, they are in a submissive position, they can't defend themselves because they are focused on the laying process. You will also see hens gang up on and peck the neck/head of a hen that is getting mated by a rooster - similar behavior. It is a fault in the behavior of the EE. The EE is trying to assert her dominance over the orpington - some pecking to show dominance is fine, but the fact that she's drawing blood is a problem - that's not normal behavior, it is too extreme.
Since it hasn't gone on long, if you interrupt this now, and can prevent it from becoming a habit for the EE, you may eventually be able to reintroduce everyone and have a peaceful flock. But there's no guarantees. The orpington may need to grow some more and get bigger before she stops getting bullied, and she'll need to be more assertive. It depends on how she responds as to whether this continues. If you remove the EE from the flock for about a month (don't let her see them), and put some pinless peepers on her right before re-introduction, she will lose her place in the pecking order, and be more focused on figuring that out for a while then on bullying the orpington - sometimes that can help stop the behavior from continuing. I'd have her wear the pinless peepers for a month or two, and then see how she is once you take them off. She has to totally stop this behavior long enough to forget about it, and that takes time. If she goes right back to drawing blood on the orpington after several months break, the EE is not right in the head, and you'll need to rehome either her or the orpington. An experienced chicken keeper told me - always solve for peace in the flock - it is SO very important!
One other thing you can do is try to make a safer/unobserved place for the orpington to lay her eggs. Like a hidden nest, where the orpington can sneak off to, and the EE doesn't notice. Also maybe nest box curtains can help. I use 5 gallon buckets on their sides in the covered run, and cover them with upside down plastic lawn chairs. I change where they point in relation to the rest of the run and whether they're behind stuff, etc, and that changes how "hidden" the hens feel. When they feel more hidden, they use that nest box more often.
