Arrange a rack in the middle of the oven and heat the oven to 350°F.

Heat 2 teaspoons of the neutral oil in a large skillet over high heat until shimmering. Add 2 cups thinly sliced yellow or red onions and cook until charred in spots, 4 to 6 minutes. Transfer to a plate.

Reduce the heat to medium-high. Add the remaining 1 teaspoon neutral oil and 1 pound ground beef to the pan. Cook, breaking the beef up with a wooden spoon into small pieces, until cooked through, about 5 minutes. Add 2 tablespoons prepared yellow mustard, 2 teaspoons Worcestershire sauce, ½ teaspoon garlic powder, ½ teaspoon kosher salt, and ¼ teaspoon black pepper. Cook, stirring constantly, until deeply browned in spots, about 2 minutes. Remove the pan from the heat.

Without separating the rolls, cut 1 package Hawaiian sweet dinner rolls in half horizontally with a serrated knife. Place the bottom half of the rolls cut-side up in a small rimmed baking sheet, 11x7-inch, or 9x13-inch baking dish.

Arrange 8 American cheese slices on the bottom half of the rolls in an even layer, overlapping the slices as needed to fit. Top with the onions in an even layer. Using a slotted spoon, transfer the beef mixture evenly over the onions. Sprinkle with 1 ½ cups shredded medium cheddar cheese and top with ½ cup sliced dill pickles. Place the top half of the rolls cut-side down over the pickles.

Brush 1 tablespoon melted butter or olive oil over the top of the rolls, then sprinkle with 2 teaspoons white sesame seeds. Cover the baking dish tightly with aluminum foil. Bake for 10 minutes. Uncover and bake until the cheese is melted and bun tops are toasted, 12 to 15 minutes. Meanwhile, make the burger sauce.

Place ½ cup mayonnaise, ¼ cup ketchup, 2 tablespoons sweet pickle relish, and 1 tablespoon prepared yellow mustard in a small bowl and stir to combine. Taste and stir in up to 1 more tablespoon mustard, kosher salt, and black pepper as needed. Serve with the sliders for dipping.