Heat butter and oil in a fry pan and cook the onion slowly until pale and soft, then cool. Combine the beef, egg yolk, capers, salt and pepper in a bowl, add the onions and mix well. Add the beetroot and juice, and mix well. With wet hands, shape the meat into 4 large, flat burgers (the traditional method) or make 8 smaller, taller patties.
Heat a ridged cast iron grill, oil both the grill and the burgers lightly, and grill them on medium heat for about 5 minutes on either side. Or heat a little olive oil in a fry pan and cook over medium heat until browned. Serve with grilled muffins and a handful of rocket leaves, sliced tomato and a dollop of mayo.