REove it whenever you see it. If you pull it by the time it gets 4 new leaves, it won't have a chance to revitaklize the nutlets.

With repeated effort -- persistence, as in never quit -- it will go away. But it won't happen with the first yank. Sorry, but this is your new hobby.

There is nothing you can spray to control Nutsedges that would be safe to use in a vegetable garden. Part of the control process is understanding how and why these sedges grow.
All sedges are bog plants, they need a fairly moist soil to get established although once established they can grow in about any soil. They tend to grow, once established, in well mulched soils and in lawns that are watered daily. Landscape fabrics do not seem to deter them since they can punch right through that stuff.
Mechanical removal, cutting the leaves so they cannot manufacture nutrients to feed the tubers which is what they grow from, is the most effective means of control.

Here is a link that might be useful: About Sedges