Chop the leek and place it in a deep frying skillet.
Add the salt, paprika, spearmint, vegetable oil, and water.
Simmer the leeks for 15 minutes under a closed lid.
Take the lid off and continue to simmer the leek until most of the liquid evaporates.
Take the pan off the stove and set it aside.
Preheat your oven to 350°F (180°C).
Crack the three eggs into a glass bowl, then season them with a pinch of salt and add 2 tbsp vegetable oil and 1 tbsp vinegar.
Beat the eggs with a wire whisk, then gradually whisk in the water.
Start to slowly mix in the flour and stir until the dough comes together.
Transfer the dough onto your work surface and begin kneading it with your hands. Keep kneading the dough until it's no longer sticky.
Divide the dough into six evenly sized balls and place it into a baking pan. Cover the pan with a towel and let the dough rest for 15 minutes.
Once the dough has fully rested, take 4 of the balls out and roll them into a circle with a diameter of 12 inches.
Bake each rolled-out pastry sheet in a greased baking pan until it becomes lightly golden on both sides. It's best to put the pan on the middle rack of your oven as this will ensure the pastry sheets bake evenly.
After you finish baking all of the pastry sheets, you should take another dough ball and roll it into a 13-inch circle.
Lay the newly rolled-out dough ball into a greased baking pan and fold its edges so they stick to the side of the pan. This will prevent the dough from shrinking while it's baking in the oven.
Scoop some of the leek filling and spread it evenly over the dough. Be careful not to add too much filling as you'll need to have enough for the other pastry sheets.
Place another pastry sheet on top and repeat this process with the rest of the pastry sheets.
Roll the last dough ball and place it on top of the leek pie. Tuck the edges of the dough so it seals the entire pie. This will trap the moisture and give the pie a tender bite.
Whisk the last egg in a small bowl and use it to brush the top of the leek pie.
Bake on the lower rack of your oven for about 45 minutes or until the top becomes golden brown.
Spray the top of the pie with some water, then cover it with a towel and let it rest for 15 minutes before serving.