I didn't cut mine back the first year. By the second season it had grown several feet and then I cut it back to about 12-18". This is now the fourth year and I'm hacking away at it like crazy! It gets huge with many stems and branches. I don't think it matters so much what you do at this point, they are pretty tough. If I were you, I'd leave it alone until this time next year.

Lisa is right; these plants are tough. Mine dies back to the ground every winter; it gets cut back to about 5 inches in late winter. As soon as the weather warms up, it takes off. It's hard to tell for sure, but if that's a dead branch, you can cut it back to new growth.

Thanks for the replies. Those branches are odd looking to me too. I think I will leave it alone with the exception of that bare limb. Ill just give that one a haircut and see what happens. Cant wait for this thing to bloom again because it both looked and smelled great last year.

You can mow them with a lawn mower and they will come back! Very tough plant if it is Buddleia davidii. Here they are evergreen and they will take over unless cut back hard (to the ground) every spring. Yours is small so you can go easy on it now but be prepared to show it who's boss!

Here is a link that might be useful: Form and Foliage

ha cant wait!

they die consistently for me in z5 ...

you might want to take that z9 advice with a grain of salt or two ...

ken

Ken maybe a ton or two! I didn't weigh in until the 5b and the 5/6 noted how tough they were, and the OP is zone 6. I actually think they are miserable shrubs here because they are so vigorous they seem to take over the world. But the best advice is from similar climes, so thanks for reining me in.
Sara

Since it's clearly alive, I can't imagine there's any danger of trimming. It looks like there are 2 (live) tall branches sticking up much higher. Unless those 2 are very sturdy, I would cut them back, just above the lower growing nodes on those branches. If they are at all floppy, they won't be able to support all of the growth they will produce, and start to lean far away from the center. If it's just leaning over another part of the bed, that might be OK, but if it's going to lean into the yard, that could get annoying.

If you are going to trim any live parts, I would do it soon before the plant wastes energy on those parts. The bonus is that the trimmed parts are extremely likely to grow if you keep them moist-not-soggy, mostly shady (until you notice new signs of growth.) With most cuttings, it's necessary to remove most of the foliage but I don't find that to be necessary for Buddleia cuttings.