I love perennial veg, but don't have nearly enough. Here's my experience in my humid continental Midwest climate z5a. Asparagus is a perennial favorite (especially Purple Passion) so I've got about 60'. Walking onions have become a staple guild plant that tolerates shade, competes against grass, prolifically propagates and makes great early green onions. Caucasian Mt Spinach grows easily, tolerates shade, modestly self-seeds, early growth is good in a mixed salad, older cooked like spinach, I'm a fan. Nettles are a wild harvested favorite, I find it a tender and mild green and have transplanted some into the timber by the house. I save the cooking water and dilute cold mint (and other) teas 50/50 and the kids don't notice. I just discovered several patches of ramps in the timber too and am very excited, they don't taste especially garlicky to me but the greens have a very rich savory flavor. My 3 year old sea kale plants were healthy but resented being transplanted and died (I still have some seed and need to experiment more). Out of 25 or so perennial kale I grew (Experimental Farm Network) a few years ago, only about 4 survived the first winter (it was a test winter -26F) and those remaining didn't survive last winter (a mild one, -12F), but they weren't well cared for so I should try again as they were good eating and we love kale (and perennial greens are my holy grail).
I was surprised that Wild arugula (random packet of sylvetta sp.) perennialized in the greenhouse (along with a few parsley plants that persisted for 4-5 years despite going to seed each year). Horseradish is a bulletproof perennial, and though one can only eat so much horseradish sauce, it's leaves make a pretty mild, acceptable cooked green. But unlike hybrid comfrey it propogates by seed as well as root fragments so keep it far from your garden.
My favorite tea is anise hyssop (Agastache foeniculum). The best is from "native" seed I harvested from a restored prairie nearby, far better than any of the half dozen "improved" varieties I've grown (granted only one or two were selected for their aroma). I've also run across A. nepetoides in the woods and field edges but have never tried it as tea. If only sacred basil was perennial in my climate!
The common daylilies have decent buds and flowers though I've never bothered to harvest in quantity and bring into the kitchen, maybe they'd be good battered and fried? I haven't tried hosta yet. Sunchokes are decent. I usually ignore in the fall and forget in the spring, but next year! I'm most interested in trying Linden, Turkish broccoli, perennial kales/greens, groundnuts and maybe a super hardy bamboo.
PS - Many mentioned berries. Here are some lesser ones I appreciate: honeyberries (shade tolerant! early ripening, many varieties, easy to propogate from hardwood cuttings in early spring, tasty if a bit fiddly to harvest, they turn color well before they're prime). Gooseberries as well as red/white/black currants are tasty and shade tolerant so they don't take up prime real estate and go in the understory.