For the fries:
2 tablespoons plus 2 teaspoons white vinegar, divided
3 Russet potatoes, peeled
Fine sea salt or kosher salt
For the onions:
2 tablespoons butter
2 large onions, quartered, peeled and thinly sliced
1 large bay leaf
White pepper and finely ground black pepper
1/2 cup sour cream
1/4 cup ketchup
3 tablespoons pickle relish, such as Wickles
1 teaspoon Worcestershire sauce
1 tablespoon safflower, vegetable or canola oil
1 1/2 pounds 80% lean ground beef
8 slices sharp American cheese, such as Cooper, mild cheddar or Swiss
4 potato burger rolls
Chopped iceberg or gem Romaine lettuce
Bread-and-butter pickle slices
Preheat oven to 425°F.
Place 2 tablespoons vinegar and about 3 cups water in a bowl. Cut the peeled potatoes first into planks then into thin fries. Add fries to vinegar bath and soak 20 minutes.
Drain fries and dry, then spread them out on a large baking sheet in a single layer. Sprinkle fries with remaining 2 teaspoons vinegar and spray with cooking spray. Season with salt and roast 20 minutes; turn fries over and roast 20 more minutes. Remove from oven and salt to taste.
While the fries are cooking, in a skillet over medium heat, melt butter for the onions. Add onions and bay, and season with salt and both peppers. Cook onions 15-20 minutes until very soft and light caramel in color. Add 1 cup of water and cook 10 minutes longer until onions are a deep caramel color and the water has been absorbed.
In a bowl, combine sour cream, ketchup, relish and Worcestershire sauce.
Heat a cast-iron skillet over medium-high to high heat with oil, 1 turn of the pan. Divide the meat into four portions and loosely roll each portion into a ball. Add balls to the hot pan and smash them into patties with a metal burger spatula. Season with salt and pepper, and cook 3 minutes then flip and top each patty with 2 slices of cheese. Cook burgers 2-3 minutes more, tenting with foil to melt the cheese.
To build the burgers, slather sauce on the bun bottoms and top with lettuce, pickles, a burger patty and some sweet onions. Set bun tops in place and serve.