For a smoky, flame-grilled flavour, grill the burger patties over an open fire. Lightly toast the inside of the rolls to prevent the bread from getting soggy.
Using your hands, combine the minced beef with the feta cheese, diced red onion, garlic, origanum and egg and generously season with salt and pepper.
Divide the mince into 4 parts and roll each piece into a ball, then form into flat patties roughly 10 cm wide and about 2 cm thick.
To help firm up the patties, drizzle with olive oil, put them on a plate, cover and place in the refrigerator until needed.
To make the tzatziki, combine the yogurt with the cucumber, garlic, lemon juice and season to taste with salt and pepper. Add more lemon juice if required. Refrigerate until needed and drizzle olive oil over the top of the tzatziki before serving.
Heat a griddle pan on a medium-high heat, brush the burger patties with oil and cook for 3 or 4 minutes on each side or to your liking. Use a spatula to lightly press down on them, making sure each burger is in full contact with the pan.
Build the burgers by topping them with crunchy lettuce, juicy tomato slices and crumbled feta cheese. Finish them off with a few dollops of refreshing tzatziki and sink your teeth into the delicious feta-melt beef patties.