Preheat oven to 190C/375F. Line a baking sheet with baking parchment paper (or use the parchment from the pastry packet)
Remove the pits from the cherries with a pitter gadget (much easier!) or carefully with a knife.
Add the cherries to a large saucepan over a medium heat with the sugar, lime zest and juice and vanilla. Bring to the boil, then reduce the heat to low and cook for 5 minutes, stirring occasionally.
Make a cornstarch slurry by dissolving it in the water, then add it to the cherry mixture and stir to combine. Bring back to the boil, heat for 1 minute, then remove the pan from the heat. It will be thick but not overly gelatinous.
Unroll the dough and cut into 6 equal-sized squares. Spoon 2 heaped teaspoons of the filling onto one side of each pastry square. Brush a little milk around the edges, fold the dough over and use a fork to crimp and seal the edges. Brush with some more milk, then use a sharp knife to cut slits in the pastry. Sprinkle with the demerara sugar and bake for 20-25 minutes, or until golden. Serve warm or cold.