Combine all ingredients in a very small pot. Bring mixture to a boil over medium heat. Boil for 30 seconds, then remove from heat and let cool completely. Pour cooled mixture through a fine-meshed sieve into a small baking dish or other freezer-safe container just big enough to hold the mixture in a shallow layer. (Protip: save the strained shallot and toss into your next salad.) Freeze the mixture, scraping every hour or so with a fork to break up the ice into small pieces, until fully frozen (probably about 3 hours). Serve in a small, very cold bowl as a condiment for oysters on the half shell.