Preheat grill on medium high heat.
Put a saucepot on the stover over low heat. Add butter, onions, salt and pepper, cover and cook for 30 minutes, stirring from time to time. Add vinegar and stir, adjusting seasoning if needed. Reduce until syrupy, additional five minutes.
Generously season burgers with salt and pepper. Grill for about 5 minutes a side until nicely browned with grill marks and cooked through. Top with raclette cheese and close the grill allowing the cheese to melt for 1 minute.
Toast the English muffins on the girl for about 1 minute a side.
Mix everything together in a bowl for the lemon herb mayo.
To assemble the burger spread the lemon mayo on both sides of the English muffin, put the burger down on bottom bun, then top with caramelized onion and arugula. Place top bun on top and serve.