A cast-iron skillet delivers the best sear for these burger patties.
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. Simmer and stir until the water evaporates, about 2 minutes. Transfer to a bowl and set aside.
Heat a griddle or skillet over medium heat; lightly brush with vegetable oil. Toast buns on the griddle, split-side down. Spread about 1½ tablespoons dressing onto each toasted bun bottom. Top with a few pickles, lettuce, two tomato slices (make sure to season with salt and pepper), another dollop of sauce, then set aside.