In a large pot, over medium heat, sweat the eschalots in olive oil until translucent. Raise the heat to high and add all of the mussels; cover and cook for 3 to 5 minute or until all of the mussels have opened.
Take off the heat and transfer the mussels to a serving dish, leaving the liquid in the pot. Return the pot to the heat and add the wine and parsley to the liquid. Bring to a boil and reduce by 1/3.
Take the pot off the heat and stir in the yogurt. Mix thoroughly. Pour the sauce over the mussels.