Add the strawberries, sugar, lemon juice, and salt to a small pot over medium-low heat. Stir the mixture until it starts to boil. Allow the filling to simmer for 5-8 minutes, stirring often. You want the berries to release their juices and concentrate a bit, but you don't want it all to evaporate. Break up bigger berries with a spoon or masher.
In a small bowl, whisk the cornstarch, water, and vanilla together to make a slurry. Stir until the cornstarch is completely dissolved – any starch that is not dissolved will make lumps in your filling.
Pour the cornstarch slurry into the strawberries, stirring constantly to prevent burning and lumps from forming. Reduce the heat to low until the mixture begins to thicken and loses its cloudiness. Cook one more minute for the cornstarch to fully cook. Remove from heat and allow to cool to room temperature, or pour into a lidded container and chill in the refrigerator until ready to use.
Assembling the Turnovers:
Preheat the oven to 400°F/200°C/gas mark 6. Line a large baking sheet with parchment paper.
Lightly dust the work surface with flour. Roll out each block of puff pastry into a 12" (31 cm) square with a floured rolling pin, starting in the middle and rolling outward. Cut each pastry sheet into 4 squares with a sharp knife or a pizza cutter; using both blocks of pastry will result in 8 turnovers. (If you're using pre-rolled sheets, roll them enough to flatten out the creases. If the sheets are rectangular, you may cut each sheet into 6 squares for smaller turnovers, or 4 rectangles which will later be folder into rectangles rather than triangles.)
Spoon 1-2 tablespoons of the cooled strawberry filling onto the middle of each square of pastry, leaving at least a ½" (1 cm.) Do not overfill or the filling will leak out. Lightly brush the borders of the pastry with milk, then fold each pastry in half diagonally so two corners meet creating a triangle. (If you cut rectangles, fold the pastry lengthwise so the 2 short corners meet.)
Crimp the edges firmly with a fork. If the fork is sticking to the pastry, dip the fork in flour, repeating as necessary. Brush the tops of each turnover with milk, then lightly sprinkle with coarse sugar.
Transfer to the prepared baking sheet. Using the tip of a sharp knife, poke 3 small slits into the top of each pastry so steam can escape. You may also use scissors to snip the small slits.
Bake for 15-18 minutes, or until the pastry is golden brown and puffed. Rest for 5 minutes on the baking tray then transfer to a wire rack to cool completely.
(Optional) For the Vanilla Glaze:
In a small bowl, whisk together the confectioners' sugar and vegan milk - add a teaspoon at a time just until you get the desired thick but pourable consistency for drizzling.
Add the glaze to a squeeze bottle with a small round tip, or a small zip lock bag (cut a tiny corner off once filled and sealed) - or you can use a spoon to drizzle a bit of icing over each turnover. Strawberry turnovers can be left covered at room temperature for about a day before becoming stale, or store in an airtight container in the refrigerator for about 5 days. The pastry will soften. To re-crisp, heat in a 350°F/177°C/gas mark 4 oven for about 5-10 minutes. See Notes below for instructions for freezing turnovers.
Unless the package directions say otherwise, frozen puff pastry can be thawed in about 4 hours or overnight in the refrigerator. Be sure to work with it while it's still cold so the fat doesn't melt. Warm puff pastry is sticky and hard to work with, plus it may result in pastry that doesn't rise enough or hold its shape.
Don't Have Strawberries?
I used frozen strawberries which are perfectly ripened before freezing, and available year round. Fresh ones also work very well if you're looking for a vegan strawberry recipe! Other types of berries such as raspberries, blackberries, blueberries, or a mix of thereof, can be used instead of strawberries.
Freezing Turnovers Before Baking: Completely assemble the turnovers but do not brush the tops with milk or sprinkle with sugar. Place the turnovers in a single layer on a baking sheet, and freeze until solid (a few hours or overnight.) Once frozen, transfer the turnovers to an airtight container or freezer bag and return them to the freezer for up to a few months.When you're ready to bake the frozen turnovers, remove them from the freezer but do not defrost them. Brush them with milk and sprinkle with sugar as directed, and bake in a preheated oven as normal but add an extra few minutes to the baking time.Freezing Baked Turnovers: Cool the turnovers completely, and then freeze them in a single layer on a baking sheet. Once completely frozen, you can gently transfer the berry turnovers to an airtight container. You can store them in a freezer bag, but they will be delicate and their tender flakes will break off when bumped by other freezer items.To prepare frozen baked turnovers for serving, thaw them at room temperature for about 30 minutes on a baking sheet, Heat them in the oven preheated to 350°F/177°C/gas mark 4 for about 5-10 minutes to re-crisp the pastry. Let cool 5 minutes and then drizzle with the icing if desired.