Put the rice in a mesh strainer and rinse with cold water several times. Set aside and let drain.
Heat the vegetable oil in a large saucepan over medium-high heat until it begins to shimmer. Add the mustard seeds and cook until they just begin to pop, about 20 seconds. Add the onion and saute until lightly browned, about 3 minutes. Add the cardamom, cloves, cinnamon, rice, the simmering water, salt, pepper and lime juice, and bring to a boil.
Reduce the heat to medium, and cook until liquid is nearly absorbed, about 10 minutes Fold in the peas, then over, reduce heat to low, and cook 8 to 10 minutes longer. Remove from the heat and let stand for 5 minutes, uncovered. Remove and discard the cardamom, cloves, and cinnamon and fluff with a fork. Transfer the pilaf to a serving dish and serve.