MAKE the Burgers: In a large nonstick skillet, heat 1 teaspoon of the oil over medium-high heat until shimmering. Add onions and ¼ teaspoon of the salt. Reduce heat to medium-low and cook, stirring occasionally, until onions are well-browned, about 15 minutes. When onions begin to sizzle loudly and look dry, add 1 tablespoon water; stir. Cook until water evaporates and onions start sizzling again. Repeat, adding 1 tablespoon water and cooking until onions are very soft and dark brown, about 3 times total. Set aside.
IN a large cast-iron skillet, heat the remaining 1 teaspoon oil over medium-high heat until lightly smoking. Season the patties with the remaining ¼ teaspoon salt and black pepper. Add the patties to the pan. Cook, undisturbed, until well-browned and crisp on bottom, about 2 to 3 minutes. Meanwhile, spread mustard on the raw side of each patty. Turn patties and cook for 1 minute on the mustard side.
FOR each burger, place 2 stacked lettuce leaves on each of two plates. Top each with 1 tablespoon of the Secret Sauce, four pickle chips, one patty, half of the onions, one tomato slice, another patty, and another 1 tablespoon of the Secret Sauce.
MAKE the Oven Fries: Preheat oven to 400°F. Cut each potato into 12 wedges. In a medium bowl, combine potatoes, oil, salt, black pepper, and onion powder; toss to coat. Spread in a single layer on a large parchment-lined rimmed baking sheet. Bake until potatoes are browned and crisp, 40 to 45 minutes. Serve with ketchup.