In a medium sized bowl, add in the ground lamb, onion, garlic, oregano, salt, pepper, parsley, and lemon zest. Use your hands to mix until just combined.
Break the lamb mixture into four, equal sized chunks and shape them into rounded patties. Aim to make the patties slightly larger than your burger buns; they will shrink a little when cooking. Press the center of each patty gently with your finger to create a little dimple. Set aside.
Set your skillet on the stove over medium-high heat and add in the oil or butter.
Once the pan is sizzling hot, add in your burgers, making sure to leave a little space between each one. If using a smaller skillet, cook the burgers in batches.
Cook for four minutes, undisturbed and flip. Cook an additional three minutes, then reduce the heat to medium. Add the sliced kasseri and cover with a lid to allow the steam to melt the cheese for one minute.
Remove the burgers from heat and assemble with toppings!