Poach the fish: Place all the ingredients for the poaching liquid, except the fish, into a 2-quart pot over medium heat. Gently warm until you begin to see tiny bubbles around the edges (180℉). Add the fish and poach until the thickest part reaches 140℉ in the center, about 5-6 minutes. Remove the fish to a large bowl, and lightly flake with a fork.
For the filling: Melt the butter in a 12-inch cast iron skillet over medium heat. Sweat the leeks for 2 minutes without browning, then add the garlic and cook another 30 seconds. Add the potatoes, salt, and white pepper and cook for 3 minutes. Place the flour in a fine mesh sieve and evenly sprinkle over the vegetables. Stir with a wooden spoon and cook for 1 minute. Deglaze the pan with the wine, scraping any bits stuck to the bottom. Grab your mesh sieve again and pour the poaching liquid through it, directly into the pan, discarding the aromatics. Reduce the heat to medium-low, add the nutmeg and mustard powder and gently simmer until the sauce has thickened and potatoes are tender, about 3 minutes. Transfer the mixture to the bowl with the fish and fold together with the tarragon and dill. Set aside to cool.
For the pastry: Sift together the flour, baking powder, and salt in a large mixing bowl. (If you don't have a sifter, give the powders a quick spin in your food processor to evenly combine and aerate.)
Rub the shortening pieces into the flour, using fingertips only, until the mixture looks crumbly. Add the milk in all at once and mix with a rubber spatula until the dough just comes together.
Lightly flour your hands and the countertop then dump the dough out onto it. Knead the dough ball 20 times, then divide into 6 equal pieces (86-87 grams each). Roll the pieces into tight balls and cover loosely with plastic wrap.
Line one half-sheet pan with parchment paper and the other with a few layers of paper towels, topped with a cooling rack.
Beat the egg with 1 tablespoon of water in a small bowl and have standing by.
Lightly dust the countertop with flour and roll one of the dough balls with a rolling pin into a 7-inch diameter circle. Spoon 1/2 cup of the fish mixture onto the center of the circle and brush the edges with the egg wash. Fold the circle in half, dip a fork into some of the flour then crimp the edges to seal. Then use the fork to lightly pierce the top of the pie a few times to allow expanding air a way out during cooking. Set the pie on the parchment lined pan and repeat with the rest of the dough and filling.
When all the pies are built, fill a 6-7-quart heavy bottom pot or Dutch oven with 2 inches of vegetable oil (about 2 1/2 quarts). Set the pot over medium-high heat and bring the oil temp to 375℉.
Carefully move the pies, two at a time, to the oil, laying them away from you to avoid oil splatters, (I find fingers are best for this, but you can use the spider or slotted spoon, especially if you briefly chill the pies first to inhibit stickage.) Fry for 2-3 minutes, flipping occasionally with the spider or slotted spoon until golden brown.
Remove the pies to the paper towel lined sheet pan and sprinkle with a little salt. Repeat the process with the remaining pies. Cool for 10-15 minutes before consuming.
Pies can be stored in the refrigerator for 3-4 days. To reheat, place the pies in a cold cast iron pan over low heat. Cover with a lid and warm through for 15 minutes, flipping halfway through. This is the best way to maintain a crisp exterior.