To marinate meat:
The day before you plan to serve the biryani, cut the goat thighs into 1½-inch pieces. Heat oil over medium-high heat in a large sauté pan. Add onions and cook, stirring occasionally, until brown and caramelized, around 20 minutes. While the onions are cooking, toss the goat with biryani masala, yogurt, ginger, garlic and salt in a nonreactive glass bowl. Add 4 tablespoons cooked onions and mix gently to combine. (Reserve remaining cooked onions.) Cover meat with plastic wrap and marinate overnight.
To prepare rice:
The next day, rinse basmati rice until water runs clear. Drain. Bring a large pot of salted water to a boil. Add cardamom, cloves, cinnamon stick and rice to the water and boil until rice is ¾ of the way cooked, around 10 minutes. Drain the partially cooked rice and spread it out to cool in a single layer on a flat surface.
To prepare potatoes:
Heat oil over medium-high heat in a medium sauté pan. Fry potatoes, turning occasionally, until they are light brown. Sprinkle sugar in the hot oil about halfway through cooking potatoes. Once potatoes are cooked, drain on paper towels.
To assemble and cook biryani:
Preheat oven to 375°. Brush a large heavy-bottomed pot with a lid with the melted ghee. Place the meat in a single layer in the bottom of the pot. Layer the fried potatoes on top of the meat, followed by the partially cooked rice. Spread the reserved cooked onions on top of the rice, and then sprinkle with saffron and lemon juice. Cover pot tightly with aluminum foil, then place lid over the foil. Place biryani in oven and bake for 30 minutes. Reduce oven temperature to 325° and bake for 1 hour, until rice is tender. Turn off the oven and leave biryani in the oven until ready to serve.
*Find the Biryani Masala recipe here.