Add the beef mince into a large mixing bowl along with the finely sliced leek, breadcrumbs, sake, soy sauce and miso paste.
In a separate mixing bowl or jug, add the eggs, 1/2 tsp sesame oil, pepper and salt and mix well.
Pour the egg mixture over the meat and mix everything together with your hands until well combined.
Form up the mixture into equal size patties about 2 cm / 1 inch thick. You should get around 5 to 6 patties depending on how big you make each.
In a large pan gently toast the burger buns butter side down until gently golden brown. Remove from the pan and pop on plates ready to stack.
Pour in that glossy 2 tbsp sesame oil for cooking and bring up to a medium high heat. Pop in your beef patties and cook for 4 – 5 minutes per side until cooked through.