Heat a large skillet over medium heat and add the oil and butter. Once the butter is melted and foamy, add the onion and stir to coat it in the fat. Cook, stirring occasionally, until they start to caramelize, about 20 minutes. Add the vinegar, scraping the brown bits from the bottom of the pan with a wooden spoon. Continue cooking until the onions are soft and deep brown, about 20 more minutes. Season with salt and pepper and reserve.

Cook the burger patties in the stove top, according to package directions. When you flip the burgers, top with cheese, cover and continue cooking until the burgers and heated through and seared and the cheese has melted.

Spread Dijon mustard on the inside cuts of the Kaiser rolls. To assemble the burgers, layer one burger patty without cheese, one patty with cheese, caramelized onions, bacon and apple slices. Cover with the top parts and serve immediately!