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Just treat them like storage onions or garlic, G_V.
Lift them. Let them cure in the sun for a day (just let them lay next to the rows they were in. Then hang them in a warm place out of direct sunlight to dry. When they have (takes a week or two), trim the stems to about an inch from the bulbs, and store in a dark place.
Shallots seemingly keep forever. Nine months or so, at any rate.
Two years ago I harvested my shallots (here in northern Europe we plant them as early as possible in spring, which means April here) and they kept for nearly two years! I dried them like Brook said and then hung them in strings, first outisde then brought them in when it got too cold.
I think your shallot butter sounds good and shall certainly try it and freeze it.
I shall also try freezing my squash, according to your directions instead of trying to give them away to people who don't want them!