Actually, I just read up on this!
Asparagus is a perennial, so it should come back!
Some other points to the article:
The first year, let all the spears shoot up and leaf out. This helps to nourish the
growing roots which, in turn, supply the rhizomes with nutrients to feed the plant.
The second
spring you can harvest some of the shoots, but when the shoots begin to look spindly, let them grow up and leaf out.
By the third
spring, the asparagus should produce spears in full force over a long season (8-12 weeks!)
It also says that by early summer, when spears are less than 1/4 in. wide, stop harvesting and let those spears develop ferny foliage (which builds food reserves for next year's crop.) In cold winter climates, leave the dried growth over winter so it can catch insulating snow, then remove the foliage in early
spring.
Hope this helps,
JoAnn