Finely chop the sausages in a food processor, mix together with the mince and all the other ingredients up to and including the pepper, knead well by hand until the ingredients have combined to form a compact mass. Divide the mixture into 4 portions, shape into burgers.
Charcoal/gas/electric grill: Grill the burgers over/on a very high heat (approx. 240 °C for approx. 2 mins. on each side. Move the burgers to the side or reduce the heat. Grill for approx. 5 mins. over a medium heat (approx. 200 °C until cooked, turning the burgers from time to time.
Mix the potatoes and salt, shape into 4 patties. Heat the clarified butter in a non-stick frying pan, fry the rösti for approx. 5 mins. on each side.
Spread the ajvar on the bread. Top with the salad, burger, cheese, rösti and gherkin, cover with the top half of the bread roll.