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1
Cover the beets with cold water in a heavy saucepan and boil until fork tender, about 1 1/2 hours. Drain them in a colander and let them cool just until you can handle them. Peel them warm (the skin slides right off if they're warm), then cut them into 3/4-inch cubes. You should have about 3 cups.
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2
Place the salt and 1 quart of the water in a 2-gallon zip-top bag. Seal the bag and massage it a few times to help dissolve the salt. Add the beets, cauliflower, onions, and radishes to the bag along with the remaining 1 quart of water. Seal the bag again, pressing out any air, so that the vegetables are completely submerged. Place the bag in a large bowl (to stabilize it) and let the vegetables sit on the counter for several hours, or refrigerate overnight. When ready to use, drain the vegetables in a colander, rinse them in cold water, and drain again.
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3
In large flameproof casserole, whisk together the turmeric, flour, sugar, mustard, and 1 cup of the vinegar to make a paste. Add the remaining 3 cups of vinegar and whisk until smooth. Over medium heat, bring the sauce to a boil and cook until it thickens, about 3 minutes, whisking continually to keep lumps from forming. Add the vegetables, stirring to coat them, and cook for 5 minutes. Remove from the heat and allow the mixture to cool to room temperature.
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4
Refrigerate the piccalilli for up to 2 weeks.
