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For the pie crust dough: In a large bowl, combine the flour, sugar and salt. Using a pastry blender, cut in the butter until it resembles coarse meal. It's okay if the butter bits are different sizes, so long as none of them are larger than peas. Combine the water and vinegar and add it, a little at a time, until the dough begins to come together. Turn the dough over itself a few times, but be careful not to overwork it. Pat the dough into a 1-inch-thick square and wrap in plastic. Chill for at least 30 minutes.
For the minted pea and potato hand pies: Preheat the oven to 375 degrees F.
In a large bowl, toss the potatoes with the olive oil and a generous pinch of kosher salt and pepper. Transfer the potatoes to a baking sheet and roast until tender, 20 to 25 minutes. Let cool to room temperature.
Meanwhile, in a small skillet over medium heat, saute the onion in the butter. Once translucent, add the garlic, scallions and lemon zest and cook for a few minutes more. Add the peas and cook for 5 minutes more. Remove the skillet from the heat and stir in the fresh mint. Season with salt and pepper to taste.
Once the potatoes have cooled, mash them up a bit with a fork or potato masher. Add the potatoes to the pea mixture and mix to combine. Taste for seasoning, adding salt and pepper as needed. Allow the filling to cool completely while you roll out the hand pie dough.
Raise the oven temperature to 425 degrees F.
On a lightly floured surface, use a rolling pin to roll out the dough into a large sheet, about 1/8 inch in thickness. Use a 3-inch round pastry cutter to make 24 pie crust rounds. Brush the rounds with a little of the egg wash.
Spoon 2 tablespoons of the minted pea and potato filling onto half of the pie crust rounds. Place one of the remaining pie crust rounds on top of each to create a sandwich. Bring the edges of the bottom rounds up to meet the top rounds and pinch them together until the hand pies are sealed. Flip over and use fork tines to seal even more. Take the pastry cutter and cut the hand pies once more to clean up the edges. Place the hand pies on a baking sheet lined with parchment paper. Use a paring knife to poke a slit into the top of each hand pie. Brush each hand pie with egg wash and sprinkle with a pinch of flaky sea salt.
Bake until the hand pies are deep golden brown, approximately 15 minutes.