Quite a bit warmer here than there. Leeks mature and the stalks dry. However the parts that sprout are small bulbs in the lower part of the stalk just above the roots. Depending on the variety, any where from one to several. Usually the more there are, the smaller they will be. If the bulb/s is/are solid, you can peel them out and replant. If those rotted there will be no new plant

Thanks coho. I appreciate the information. I'll check for any small bulbs. I started some more seeds, just in case.