Preheat the oven to 450 degrees F.
Toss the cauliflower with the ghee, curry powder and 2 teaspoons of the salt, and then transfer to a foil-lined baking sheet. Roast until just tender and slightly charred, stirring occasionally, about 20 minutes.
Place the potatoes in a large pot and cover with 3 inches of cold water. Stir in the remaining 1 tablespoon salt and bring to a boil. Reduce the heat to medium and simmer until the potatoes are tender, about 10 minutes. Drain and transfer to a large rimmed baking sheet, drizzle with the white wine vinegar and let cool slightly.
Combine the potatoes and cauliflower in a large bowl. Toss with the peas, cilantro, mint, ginger, garlic, onions and Cilantro Emulsion until thoroughly combined. Season with more salt and pepper, if needed, and serve.
For Cilantro Emulsion: Bring 1 quart water to a boil with the salt in a small saucepan. Add the egg (still in the shell) and simmer over moderately high heat, 5 minutes.
Transfer the egg to a bowl of cold water using a slotted spoon and let stand 3 to 4 minutes. Crack the egg all over and gently peel under warm running water, keeping it whole.
Combine the poached egg with the cilantro, lemon juice, ginger and garlic in a blender. With the blender running, slowly begin drizzling in the olive oil until emulsified. Season with the white pepper and more salt, if needed.