Step 1 Cut the vegetables into bite-sized pieces: the cauliflower into florets; the radishes in halves or quarters, depending on their size; the carrots in half lengthwise and then crosswise into 1-to 1 1/2-inch sections; the turnips into bite-sized wedges. Combine the vegetables in a large, non-aluminum bowl.
Step 2 Heat the oil to smoking in a small saucepan over medium heat. Remove from the heat and let cool a few minutes. Add the turmeric and asafetida, swirl the pan to mix and let cool. Add the ground mustard seeds, salt, cayenne and chiles and pour the cooled oil over the vegetables. Stir with a wooden spoon to coat the vegetables. Add the vinegar and lemon juice and stir well. Spoon the vegetables into 2 clean 1-quart jars and set on sunny windowsill or in a warm, dry spot in the kitchen for 2 to 3 days. Then refrigerate and eat within 3 days.