Toss together the onions, fennel and cauliflower with 2 tablespoons of the salt in a colander and set in the sink until they wilt, about 45 minutes. Rinse thoroughly.
Heat the olive oil in a large saucepan or Dutch oven over medium heat and add the turmeric, stirring until the oil is an even color, about 30 seconds. Add the ginger, mustard seeds, fennel seeds, crushed red pepper, garlic and carrots. Cook, stirring, until fragrant and the vegetables are just tender and wilted, about 2 minutes, and then add 2 1/2 cups of water, the vinegars, brown sugar and remaining salt. Bring to a boil, and then remove from the heat and stir in the cauliflower mixture. Let cool to room temperature. Transfer to a sealed container and refrigerate for 24 hours. The piccalilli will keep for 1 week tightly sealed in the refrigerator.