Those are the scapes. Funny looking, right? Bittman's pesto is an easy one: into the food processor go 2 cups of garlic scapes (or basil, for the traditional recipe), a handful of pine nuts or walnuts (I didn't toast them, Bittman doesn't say to, but I think I will the next time) and olive oil plus a pinch of salt. Turn on the machine, add a bit more olive oil while it's working, and you're pretty much done. The last step is to add the grated cheese, right before serving.
This stuff is really good: it tastes fresh, spicy, and yeah, incredibly strong in the garlic department. Next time I think I'd combine the scapes and basil, as I think they'd work well together. That is, if the scapes are around for long enough. If not, I'll just have to try the traditional pesto. That's one of those good problems.