Heat the olive oil in a large skillet over medium-high heat. Add the onion and cook, stirring, until it starts to brown, 3 to 4 minutes. Add the sugar and 1/2 teaspoon salt, reduce the heat to medium low and cook, stirring occasionally, until deep golden, 15 more minutes. Add the chicken broth and 1 teaspoon Worcestershire sauce and simmer until the onion is tender and the liquid is almost evaporated, 8 minutes.
Preheat the broiler. Mix the beef, onion powder and the remaining 2 tablespoons Worcestershire sauce in a bowl with your hands. Form into four 3/4-inch-thick patties and place on a broiler pan. Make an indentation in the center of each with your thumb; season the patties with salt. Broil, turning once, 5 minutes.
Place the buns cut-side up on a baking sheet. Sprinkle with both cheeses and broil until melted, about 1 minute. Spread mustard on the buns; sandwich with lettuce, the burgers and caramelized onion. Serve with potato chips.