In a large bowl, combine your flour, egg, and water. Combine with chopsticks, a wooden spoon, or your hands.
Once a rough dough has formed, knead the dough for 5 minutes. The dough shouldn't stick to your hands, if it does, then add in more flour. Seal with cling film and set it aside while you make your filling.
In another large bowl, combine your beef mince, oregano, salt, feta cheese, grated potato, and garlic. Mix thoroughly with a wooden spoon, fork, or your hands. Then set it aside while you make your wrappers.
Get your dough, knead it for another minute, and then shape it into a doughnut by poking a hole through the middle. Widen the hole, making the outside thinner. Then slice the doughnut and form your dough into a sausage shape. Slice the dough into 14-16 pieces.
Flour your surface and then roll out each piece of dough into a thin circular wrapper.
Place a heaped tablespoonful of the filling into the centre of the wrapper and fold over into a semicircle. Use your index finger and thumb to crimp and twist the edge, tucking the ends beneath. Repeat this for all your dumplings and set them aside underneath a slightly damp tea towel.
Get a non-stick pan and drizzle in some oil. Place it on medium heat.
Add in your dumplings (you might have to cook them in two batches). Pour in 150ml water and add on your lid. Cook for 10 minutes or until the water evaporates (if the water evaporates quicker than 10 minutes, add in some more water).
Meanwhile, make your tzatziki by combining greek yoghurt, garlic, grated cucumber, mint, pepper, and salt in a bowl. Give it a good mix and you're ready to serve up!
Once your dumplings are cooking and slightly crisp on the bottom, remove and serve up on your plate of choice. Top with tzatziki, chopped tomatoes, sliced red onion, and mint leaves. Enjoy!