The first year I have found they do lay almost daily. I was amazed.
The second year mine are laying about half that. But mine have been molting and so they are just kind of restarting back up. I am eagerly anticipating winter to see how they do the second winter.
I wouldn't be without them in a flock. They are great!
I was surprised, my EEs lay 6-7 days a week! Now 1 of mine, her eggs are not getting very large, still small size but the younger one who started laying 2 weeks ago, her eggs are already getting larger...medium size. So they are good layers, just not BIG eggs so far.
I only have one EE and she was laying 6-7 days a week when she started laying. She now 11 months old and is settling into a slightly slower routine of 4-5 days a week.