For the burger patties, combine all the ingredients in a large bowl with your hands and separate into 6 even patties.
Add 1 tbsp oil to a large pan or grill on high heat and cook on both sides until nicely coloured and cooked through. Place a slice of cheese on each patty and allow to melt.
Meanwhile, for the caramelised onions, gently saute onions in oil on a low heat until slightly softened and add balsamic vinegar and sugar. Let cook, stirring occasionally, for 15-20 minutes. Remove from heat.
To make the sauce, combine sour cream and prepared horsreradish in a small bowl and set aside.
To assemble the burgers, just add lettuce and sliced tomato on a bun and place the patty on top. Pile on onions and dollop the horseradish sauce on top. Repeat with remaining burgers and add the top bun. Serve.