Heat a tablespoon of olive oil in a large, heavy-bottomed skillet over medium heat. When the oil is hot, add the diced yellow onion and a big pinch of salt. Cook, stirring infrequently, until the onion is soft and slightly caramelized, about 20-25 minutes. If the onion seems to be browning too quickly, reduce the heat.
When the yellow onion is caramelized, add the shallot and the white bottoms of the scallion to the pan. Cook, stirring occasionally, for an additional 3-4 minutes, until the shallots and scallions have softened. Stir in the soy sauce and rice vinegar.
In a large mixing bowl, combine the yogurt and the onion mixture. Stir in the green parts of the scallions, reserving a few for garnish if you like. Season with salt, pepper, and additional olive oil to taste.
Spoon the mixture into a serving bowl or storage container, and allow to chill in the refrigerator, covered, for at least an hour. Serve with your favorite chips or vegetables.