Peel and slice the onions. In a large, heavy-bottomed skillet, heat the olive oil over medium-low heat. Add the onions and thyme, stir to coat with the olive oil and place a tight fitting lid on the pan. Cook for 3-5 minutes, stirring occasionally, until the onions are soft and translucent. Do not brown the onions. Remove the thyme sprigs and discard.
Transfer the soft onions to a food processor or blender. Add the kosher salt and vegetable broth and puree until smooth. Transfer to a storage container and refrigerate at least 3 hours or overnight.
If soup separates overnight, stir it until it's smooth again, then ladle into bowls and garnish with chopped chives.