In a large saute pan over medium heat, add the olive oil. Add the thyme, shallots, garlic and all the varieties of onions. Saute, stirring constantly. (Onions absorb oil quickly, so add more if necessary.) Continue to cook until the vegetables are lightly browned, about 15 minutes. Remove from the heat and season with salt and pepper. Let cool slightly.
In a medium bowl, add the yogurt and cream cheese and stir together. Add in the onions, scallions and chives. Stir well to combine.