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1
Mix together the water and vinegar in a measuring cup and keep cold.
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2
Combine the flour, sugar and salt in the bowl of a food processor and pulse a few times to combine.
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3
Scatter the cold butter over the top and pulse a few more times until the mixture resembles coarse meal.
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4
Add the water-vinegar mixture a few tablespoons at a time and pulse until the dough just comes together.
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5
Transfer the dough to a lightly-floured surface and knead gently until it just comes together.
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6
Form into a rectangle and cover with plastic wrap.
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7
Refrigerate for at least 1 hour and up to 48 hours.
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8
While the dough is chilling, combine the fruit and sugar in a small saucepan.
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9
Cook over high heat until it comes to a boil, the fruit starts to break down and the juices start to release, about 8 minutes.
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10
Stir together the lemon juice and cornstarch until combined.
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11
Add the cornstarch mixture to the pot while it is still boiling and cook until it begins to thicken, about 1 minute.
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12
Stir in the jam and the lemon zest.
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13
Transfer to a bowl, and refrigerate until cold.
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14
Preheat the oven to 375 degrees F. Line baking sheets with parchment paper.
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15
Roll out half of the dough on a lightly-floured work surface into a large 1/8-inch-thick rectangle.
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16
Trim the sides with a knife so that you have a 9- by 8-inch rectangle with straight edges.
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17
Along the length, cut the rectangle into thirds so that you have three 3-inch strips.
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18
Then, cut the strips into fourths so that you have twelve small 3- by 2-inch rectangles in total.
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19
Carefully transfer these rectangles to one of your prepared baking sheets.
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20
Repeat this with the other half of dough.
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21
Gather the scraps of both halves and re-roll to create more rectangles (you will get 6 to 8 more).
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22
Spoon a heaping teaspoon of strawberry filling in the center of half of the rectangles so that it is slightly heaped (do not spread it out).
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23
Make sure not to over-fill them and leave an about 1/4-inch border.
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24
Lay another rectangle over the filling and press gently around the edges to seal slightly.
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25
Use the tines of a fork to press the two layers of dough together and seal completely.
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26
Place the baking sheet with the pastries in the fridge until chilled, about 20 minutes.
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27
Lightly brush the tops of the pastries with milk.
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28
Use a toothpick to poke 8 holes over the top surface to allow the steam escape during baking.
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29
Bake until golden around the edges, 15 to 20 minutes.
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30
Transfer to a wire rack to cool.
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31
Stir the milk into the confectioners' sugar until smooth (add a drop or 2 of water if you need to loosen it).
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32
Drizzle over the cooled pastries and serve.
