Looks like the eggs one of my EE pullets has been laying. Her first egg was like that, wrapped in a slimy membrane. And the second one. She's my worst layer (maybe 1-2 eggs a week), and I'd say almost half of her eggs have been like that. Fortunately the last three have been normal, except for the little extra bumply calcium deposits and thinnish shells. But for a while there I was afraid we'd have to cull her because I was afraid she would become an internal layer or become egg bound.