Put the mince in a mixing bowl. Add all ingredients and combine. Season with salt and pepper, then mix well with your hands.
Form 4 patties and set aside or chill until you're ready to cook them.
Make the feta sauce: mix the feta with enough yogurt to get a textured sauce. Add the lemon zest & juice, mint, salt & pepper. Taste, and adjust to your liking (you can add a pinch of cayenne if you want it spicy). Set aside.
Heat your BBQ, grill or griddle pan.
Brush the patties with a little oil, then cook over medium heat for 3-5 minutes on each side, depending on how well cooked you like your burger.
Cut the buns in half, then toast or grill them and set aside.
When the patties are cooked to your liking, move them to a plate to rest for a couple of minutes.
Meanwhile assemble the burgers: spoon some feta sauce on the bun halves, add a few lettuce and tomato/onion/cucumber slices, place the patties on top, then add the other half of the buns.
Enjoy!