In a medium bowl, cover the rice with cold water. Set aside.
Line a plate with two paper towels. Heat the olive oil in a large pot over high heat. Add 1 chopped onion and cook, stirring constantly, until the onions are deeply browned and start to crisp around the edges, about 20 minutes. Transfer to the plate and set aside. They will continue to crisp as they cool.
In another pot, add some oil and the onions and saute until golden brown. Add the lentils then add water and stir to combine. Bring everything to a boil, then reduce the heat to medium-low and cover with a tight-fitting lid. Cook for 15 minutes.
Drain the soaked rice, rinse and transfer it to the pot with the lentils along with the salt. Stir once, then cover again with a tight-fitting lid and cook undisturbed for 15 minutes.
Remove the pot from the heat. Rest, covered, for 5 minutes longer. Fluff the rice and lentils with a fork to combine.
Spoon the crispy sliced onions on top of the mujadara. Serve warm, with Greek yogurt sauce if desired.
