Combine the lentils and 2 cups of water in a pot and cook over medium heat for 10 minutes. Strain lentils and set aside.
While the lentils cook, melt the butter in a large pan over low heat. Add the onions and the vinegar. Cook for 30 to 40 minutes, stirring frequently until onions are brown and caramelized
Stir the salt, pepper, cumin and rice into the pan and cook for 1 more minute.
Combine the remaining water and the vegetable stock, then add half of the mixture to the onion mixture 1 cup at a time. Allow all of the liquid to be absorbed before adding the next cup.
Stir the lentils into the rice, then continue adding the remaining liquid one cup at at time until absorbed.
Divide the mujadara into 8 bowls and top each with a dollop of yogurt and a sprinkle of parsley and pistachios before serving.