Clean, wash, pat dry, and cut the vegetables.
Boil water in a deep sauceppan, add turmeric and salt to the boiling water.
First, add the cauliflower florets in the boiling water and blanch for 2 minutes or till tender (al-dente). Transfer to a colander. Similarly, blanch the carrots and turnip till al dente, drain, and transfer to the same colander as cauliflower. Make sure not to cook the vegetables while blanching.
Spread all the blanched vegetables on a large/clean/dry baking sheet or tray lined with a cheesecloth/ muslin cloth. Sundry or air dry the vegetables. I put them under the fan at high speed for 2 hours.
After drying, excess moisture will evaporate from the vegetables and they will be dehydrated.
Meanwhile gently pound the mustard seeds in a stone mortar and pestle. You can do the same in a spice grinder as well. Pulse mustard seeds once in the grinder. Collect in a bowl and set aside.
Heat mustard oil in a pan over a high flame. Once the oil starts fuming, turn off the heat. Add asafoetida, fennel seeds, and nigella seeds. Stir to mix. Allow the tempered oil to cool down completely.
After dehydrating the vegetables transfer them to a wide mixing bowl. Add ginger juliennes, sliced green chili, sliced lemon (discard seeds and white pith), crushed mustard seeds, salt, pickle masala, and mix nicely.
Pour tempered mustard oil, white vinegar, and mix the pickle using a spoon or wear cooking gloves to mix the pickle. Taste the pickle for seasoning, if required add more spices/seasoning according to taste, and mix one more time nicely.
Take a clean, dry jar and transfer the pickled vegetables into the jar. Seal the jar with a tight fitting lid.
Allow the pickle jar to sit at room temperature for 2 days. You can also keep the jar under the direct sun rays for a day or two. Shake the jar once or twice a day.
Gobhi Gajar Ka Achaar is ready to be served. This pickle stays good at room temperature for 10 - 15 days.