After eating the last pickle save the jar of pickle juice. Then when a broccoli stem becomes available cut the tough outer skin off, chop it up and toss it in the pickle juice. Works well. They reach a taste that’s very close what the pickles tasted like. After 2 or 3 cycles of that the pickle juice starts losing its strong punch. Adding vinegar and a sweetener can help at that point if you don’t have more pickle juice by then.
Otherwise broccoli stems are not too versatile. They’re not that great in veg. stock because they bring a bit of bitterness. So I only use like ½ a stem in a pot of broth (which is wholly from veg scraps).
My next experiment (untested): reusing juice from a jar of jalapẽnos to pickle broccoli stems.
I’ve never had luck pickling broccoli, I confess. I usually slice the stems thin and blanche them then eat them with butter and salt.