Bring a medium pot of generously salted water to a boil.
Stir in the rice, return to a boil, then lower the heat to a steady simmer.
Cook white rice for about 5 minutes or brown rice for about 15 minutes. The rice will still be firm and only partially cooked.
Drain well and set aside.
In a large bowl, whisk together 2 tablespoons (30 ml / 1 fl oz) of the oil, the yogurt, lime juice, and curry powder.
Season with salt and pepper and continue whisking until the mixture is completely smooth.
Add the drained, par-cooked rice to the yogurt mixture. Use a fork to gently toss and fold, ensuring every grain is lightly coated.
Put the remaining 2 tablespoons (30 ml / 1 fl oz) of oil in a large, heavy-bottomed pot (a Dutch oven is perfect) with a tight-fitting lid.
Heat the oil over medium-high heat.
Add the rice mixture to the pot, pressing it down firmly and evenly with the back of a spoon or a spatula to form a compact layer.
Wrap a clean kitchen towel around the lid of the pot, gathering the corners on top so they are away from the heat source. This will absorb condensation and ensure a crispy result.
Cover the pot tightly to seal the rim.
Listen for a sizzle.
After 3 to 5 minutes, once you can smell the fragrant spices, turn the heat down to the lowest possible setting.
Cook, completely undisturbed, for 30 minutes. The rice should smell toasty, but not burnt.
Remove the pot from the heat and let it sit, still covered, for another 5 minutes to set.
Carefully remove the towel-wrapped lid.
Place a large serving platter upside down over the pot. With oven mitts, firmly grasp the pot and platter together and confidently flip them over. If the rice crust comes out in a single golden cake, celebrate! If not, simply use a spatula to scrape the remaining crispy bits from the pot and arrange them on top of the rice.
Serve immediately.
Do not lift the lid while the rice is steaming on low heat. Trapping the steam is crucial for cooking the rice through while the bottom gets perfectly crispy.