Over a sink, wrap the grated beetroot in two layers of J-cloth and squeeze out as much liquid as possible. I initially used one layer of J-Cloth and it ripped, so I really advise you to use two layers! Also, the more liquid you manage to get out, the easier it will be to shape and fry the burgers later on.
In a large bowl, mix the beetroot, spring onions, garlic, mint, lemon zest, half the lemon juice, 2 tablespoons of the plain flour, the egg, along with a good pinch of salt and pepper. When well combined, stir in the feta.
Form the mixture into 6 burger-shaped patties and coat them with the remaining flour (by putting the flour on a plate). This will be a delicate process. But it helps to shape the patties into firm balls first and then flatten them slightly. When coating them with flour, be careful to be decisive (and not to move the patties around too much). Coat the top and the bottom by turning the patties over. And coat the sides by applying the flour with your hands.
Heat a large frying pan over medium-high heat and add 4 tablespoons of olive oil. Fry the patties for 6-8 minutes on each side until crisp on the outside and cooked through. It will at first seem as if they will fall apart. But if you make sure to really let it fry nicely before you turn them over and if you turn it over with a confident flip, you should be alright.
Mix the remaining olive oil and lemon juice with the salad leaves. And add a pinch of salt and pepper.
Serve the burgers in buns with a bit of mayonnaise on top. And salad and crisps on the side.