Melt the butter in a pan over medium heat. Add the sugar and onions and sauté, stirring constantly, for about 15 minutes, or until the onions are soft. Pour beer over the onions a little a time, letting it boil off completely before adding more. Keep going until the onions are caramelised. Season to taste with salt and pepper.
Heat a grill pan until it is smoking hot. Grill the steaks for approx. 2 minutes on each side. Top each steak with cheese, season with salt and pepper and set aside to rest. Brush the mushrooms with oil and grill them.
Split the buns and warm or toast them. Spread the buns with mayonnaise and top with rocket, steak, mushrooms and onions. Serve with chili-fries and extra mayonnaise.