Punk-rock drummer and former fine-dining pastry chef extraordinaire, total badass and wearer of paper soda-jerk hats — if you were looking for someone to give vegetarian fast-food a spectacular high-low makeover, to make it cool, cravable, and also, you know, nutritious, you couldn’t do much better than Brooks Headley. Everything on his Superiority menu — veggie burger, faux Sloppy Joe, burnt-broccoli salad — is mysteriously satisfying and as good as you’ve heard, except the Superiority Wrap (a.k.a. the Hippie Wrap), which is better than you’ve heard. Nor do daily specials like vegan pump-cheese nachos disappoint. Have an expert Arnold Palmer while you wait for the savory stuff. Then take your salubrious fast-food feast to a Tompkins Square Park bench, or, if one’s available, grab an old-fashioned swing-tray seat at the restaurant and imagine you’re dining at the late, great, decidedly nonvegetarian Prime Burger on 51st Street.