For the thousand island dressing, combine all ingredients in a large bowl. Fold until evenly mixed. For the burger, in a large skillet, add vegetable oil over medium heat. Add onions and 3/4 teaspoon salt, cover, and cook, stirring occasionally, until golden and soft, about 20 minutes. Uncover, increase the heat to medium-high, and continue to cook, stirring often, until caramelized, about 8 minutes. Add 1/4 cup water to skillet, scraping browned bits from bottom of pan.