1. Bring a medium pot of salted water to a boil. Stir in the rice and boil until just done, about 10 minutes. Drain the rice, return to the pot, and cover to keep warm.
2. Meanwhile, in a large frying pan, melt the butter with the oil over moderately low heat. Add the onion and cook, stirring occasionally, until translucent, about 5 minutes. Add the garlic and ginger and cook, stirring, until fragrant, about 1 minute. Stir in the cumin, turmeric, curry powder, and cayenne and cook, stirring, for 1 minute longer. Add the potato, carrots, water, and salt. Increase the heat to moderately high and simmer until the vegetables are tender and no liquid remains in the pan, about 10 minutes.
3. Stir the peas into the other vegetables and remove the pan from the heat. Stir in the yogurt and rice and serve topped with the jalapeño, tomato, and cilantro.
Wine Recommendation: The sweet, floral perfume of basmati rice calls to mind the similar aromas of Vouvray. A demi-sec will strike just the right balance with the slight heat of the biryani.