Place the potatoes, cauliflower florets, carrot, and peas into a microwave-safe bowl, cover with plastic wrap, and microwave on High until the vegetables are very hot and starting to soften, about 2 minutes. Remove the plastic wrap, and drain the vegetables in a colander.
Place the vegetable oil in a large skillet, and heat over medium heat. Cook and stir the onion until it turns golden, about 10 minutes, and stir in the cumin seed, black mustard seed, and bay leaves. Cook and stir until the seeds begin to sputter, about 30 seconds, and then add the green chiles, garlic, and ginger. Cook and stir until the garlic begins to brown, about 1 minute.
Stir in the ground cumin, curry powder, and chili powder, and then add the partially cooked potatoes, cauliflower, carrot, and peas. Cook and stir until the vegetables are tender and coated with spices, about 30 minutes. Sprinkle with cilantro leaves.