Q.After harvesting the sunflower what do I do with the stalk?
I grown sunflower seeds and now I’m not sure what to do with the stalks. Do I cut them down or do I leave them for next year? Note, this is my first time growing them.

Certified GKH Gardening Expert
They won't, likely, do anything else for the year. You can cut them down at anytime after harvest, unless you purchased a perennial cultivar, specifically. That appears to be an annual sunflower, so cutting it down will be the appropriate action.
Here is an article that will offer more information on sunflower care: https://www.gardeningknowhow.com/ornamental/flowers/sunflower/growing-sunflowers-in-your-garden.htm