In a large bowl, stir together the flour and the ½ teaspoon of salt. Slice the cold butter into ¼-inch cubes and add them to the flour. Use a pastry blender to cut the butter into the flour, until the mixture looks coarse.
Add ¼ cup of the ice water to the mixture and toss it together with a large spoon. Continue adding water 1 tablespoon at a time until the mixture holds together when you squeeze some in your hand.
Turn the mixture out onto a work surface. Knead the dough mixture together 4 or 5 times until it has come together into a smooth dough. Divide the dough in half and flatten each half into a disk. Wrap both disks in plastic wrap and refrigerate them for at least 30 minutes.
Make the filling:
Trim the root ends of the leeks and trim off most of the dark green leaves at the top. Slice the leeks in half lengthwise, then slice them crosswise into small pieces. Run your knife through the leeks a few times to chop up the slices.
Place the sliced leeks into a colander set in a large bowl (or a salad spinner) and fill the bowl with cold water. Swish the leeks around in the water to wash them, then drain. Repeat this step again, draining very well to remove as much moisture as possible.
Wash and peel the potatoes. Cut the potatoes into 1½-inch cubes and place them in a pan of cold water. (The water should just cover the cut potatoes.) Bring to a boil and cook for about 5 minutes until the potatoes are just tender. Drain and set aside.
In a large skillet, melt the 4 tablespoons of butter with the olive oil over medium-low heat. Add in the leeks and sauté them for 5 minutes until softened. Sprinkle the ¼ cup of flour over the leeks and stir them for about 2 minutes until the flour is absorbed and has coated the leeks.
Slowly pour in the stock, half and half, and teaspoon each of salt and pepper. Increase the heat to medium and bring the mixture to a simmer. Continue to simmer and stir the filling for about 3-5 minutes longer just until it has thickened.
Remove the pan from the heat. Stir the cooked potatoes into the mixture, then allow the mixture to cool to lukewarm.
Assemble the pie:
Preheat the oven to 425° F. Have a 9-inch pie dish ready: if using a glass or ceramic pie pan move the rack to the lower half of the oven.
Unwrap one refrigerated dough disk onto a lightly floured surface and roll out to about ¼-inch thickness. The dough should be roughly 13 inches in diameter. Lightly fold the circle in half and then in half again. Place it in the pie dish with the point of the triangle in the center and unfold to fit the pie dish. Gently fit the dough into the pie dish with overhang all around. Trim the overhang to about 1½ inches.
Pour the cooled leek and potato filling into the pie shell.
Take the other dough disk from the fridge and roll it out on a lightly floured surface to ¼-inch thick and 15 inches in diameter. You can make cut-outs in the dough now or use a knife to cut slits in the pie after it is assembled.
Carefully lay the dough over the top of the pie dish. Trim the edges to be just slightly larger than the bottom overhang. Roll both the lower and upper crust edges under, all around the pie to make a thick edge. Crimp the edge all around. Cut a few slits in the top crust for venting.
Beat together the egg and ¼ cup of water. Brush this wash over the top crust using a pastry brush. Sprinkle the Maldon Sea Salt Flakes over the top.
Bake the pie for 25-30 minutes until the crust has browned and filling is bubbling. Remove from oven and let rest for 10 minutes before slicing.