I love the pesto idea. If you’re under real scoreboard pressure to use it or lose it, I’m thinking you could buy yourself a decent amount of time just by making a basic ‘pre-pesto base’ of the blitzed rocket and some oil and storing in jars. Give you some time to adjust and vary the flavour profile as you use it.
I think it’d also work great as raw loosely chopped leaves in burritos, though granted that’s pretty much just another ‘salad’ instance.
I noticed there was a theme of basically putting hot meat on arugula and letting the leaves wilt. Even the sheet pan chicken and bread salad was along those lines. I’m certainly trying a few of these ideas soon.