After your plants have browned and been removed just throw it on in copious amounts. If you live where it doesn't get cold enough for the plants to brown cut the plants down about the first of the year and do it then. Do it before the new shoots begin to emerge.
You can cut them down now if you like but I always waited as long as possible, probably just procrastinating. Even In our zone of 8b winter really slows down the sugar making capabilities of the ferns so there really isn't much to gain by waiting until the first of the year. And it will give the compost that much longer to do its magic.
Mulch is mainly used for water retention, weed prevention and to help in soil temperature control. Your cold temps. will not damage the root system of your asparagus. Adding mulch is nice but not required. I would put no more than 3 or 4 inches and about once every 2 weeks I would wet it down with diluted molasses, 2 oz per gallon of water.
Molasses doesn't do anything for plants. Molasses is one of the best food sources for soil micro-organisms, the same organisms that break down organic matter in your soil. The same organisms that make nutrients available to your plants. Molasses when applied to substances like hay makes it decompose faster, turning the mulch into compost faster than just letting it sit on the soil surface. You cannot have too many of these fungal and bacterial organisms in your soil and molasses greatly enhances their numbers.
You can use the food grade molasses but it costs a lot more. Also, there is sulfured and non-sulfured molasses. The sulfured molasses is mainly used as a cattle feed supplement and is the cheapest. Horticultural molasses does not have sulfur added. Most if not all real nurseries will have molasses or they can easily get it. I buy it by the gallon and it cost about $12. The brand name I use is by Medina.
