What is this thing?

Trial and error is my plant-shopping rule. I also make it a point never to learn from any of my mistakes. Sometimes, however, a plant purchased on a whim is surprisingly successful. Take this thing, whatever it is (pictured above). Sold by a local nursery as a “perennial heliotrope”—yeah, I don’t think so either—I bought it in the hope that it might form a nice centerpiece for my big easeway planter.

(These were installed as a block club effort to have continuity up and down the street for Garden Walk and ongoing beautification. However, the plants mandated for these—canna—take far too long to grow and flower in the shade I have.)

Anyway, I took it home, planted it in the container, saw that it was supposed to grow six feet tall (I remember everything from the label except the name), and thought better of it, replanting it in a side garden near the front of the GWI property. I really didn’t think it would survive, and didn’t much care. I am the quintessential consumer, even for plants. Once the initial frenzy has calmed, my interest in my new possessions wanes quickly.

Yet, here it is, apparently thriving (what you see is only one half of the plant). The stingy little white flowers do have a scent faintly reminiscent of heliotrope, but I have white heliotrope: its leaf form is much different than this. And this is quite tall—perhaps five feet at least—and obviously perennial. I rather admire the foliage and the stature of the plant, if not the flowers. It is an interesting counterpart to the martagon lilies planted in front of it (not visible).

So, anyone know? I’m sure I’ll be embarrassed when it turns out that this is some common plant with which everyone else is familiar.

Oh, and sorry for the bad photograph. I am not a photographer; this is not a photo-blog. I blame the camera.

UPDATE
THANK YOU, ANNIE IN AUSTIN! We have our answer—see her comment below. It's all coming back to me now.

Yes, that was it. Now I can buy more and plant a whole grove of it. It's actually nicer than the hideous picture might suggest.