Whenever I make slaw or have occasion to make something with cabbage, I always look forward to the “Chef’s Morsel” the core. It’s hard and crunchy, cool and sweet, with a peppery finish. I like them with or without salt, and I get mad if someone tosses it out. My Mom and Granny also do this, so that’s where I got it from. Anyone else like the cores or do you think they go in the trash?
I eat all parts of cabbage, however only the outer layers of iceberg lettuce are edible.
They get placed under whatever I am making with cabbage and cooked into the sauce.
Mmmmm. Nothing like the kinda-sweet, kinda-peppery, kinda-creamy but definitely crunchy delicacy of a cabbage core! With salt, please!
When my sister and I were kids, neither of us were big on veggies, but we’d fight over the damn cabbage core! 
I always cut up the whole thing, cept for the hard end part :dubious:
Slice 'em thin and cook them with the leaves.