Pick through the mung beans and quinoa and rinse them under cold water.
Heat the oil in a pot over medium heat and add the onions. Cook until translucent, about 5 minutes. Stir in the garlic, mung beans, quinoa, turmeric, and dill, and cook for a few minutes until heated through. Add the stock and bring to a boil, then cover and cook at a very gentle boil, stirring occasionally, for 40 minutes. The beans should be starting to split open.
Add the greens to the pot and return to a boil, them reduce the heat and simmer, covered, for 10 minutes, until the greens are tender. Add salt and season to taste. Ladle the soup into bowls and squeeze in equal amounts of lemon or lime juice. Top each bowl with a tablespoon of yogurt, and serve.