Late Fall (October-December).
Brussels spouts are at their best after frost. They're very cold hardy and their flavor improves as the temperatures get colder.
Brussels Sprouts on the stalk will keep for several weeks in the refrigerator or another cold place in your house (perhaps the garage or barn). If you don't have space in your fridge or elsewhere, knock the sprouts off the stalk and store in a plastic bag in your fridge for about 2 weeks. Cut the stalk up with branch loppers before composting.
For longer storage, wash and trim off outer leaves and stem, if necessary, and sort for size. Blanch in boiling water, 3-5 minutes depending on size. Cool immediately, drain, pack (no headroom necessary) and freeze.
Culinary Tips & Recipes
Check out this incredible NY Times guide to cooking Brussels Sprouts
Root 5 Farm Brussels Sprouts Recipes
Brussels Sprouts Gratin