In a large pot or Dutch oven, heat a swirl of olive oil over medium. Add onions and mushrooms and stir to coat. Reduce heat to medium-low and cook until onions take on a nice brown color, approximately 30 minutes.
Add stock and increase heat to just bubbling. Wash and chop greens and add to the soup. Reduce heat to medium and cover soup. Let cook until greens have wilted, about 10 minutes.
Puree soup and return to heat. Stir in paprika, yogurt, and lemon juice, then season to taste. Alternatively, you can leave the yogurt out until just before serving, and then add a swirl into individual bowls.