Preheat the oven to 400 degrees F, with the oven rack in the middle position. Line 2 baking sheets with parchment paper.

Put the pitted cherries, sugar, lemon juice, vanilla, and salt in a medium bowl, and toss to combine. Let the mixture sit for 5 minutes, and then put it into a strainer set over a bowl. Let the cherry juice drain, and set the juice aside for later. Put the strained cherries back in their original bowl.

Gently flour your work surface, and roll each piece of the pastry dough into a 10-inch square. Cut each square into four 5-inch squares, for a total of 8 squares.

Place 2 tablespoons of the cherry mixture into the center of each square of dough, and then brush the edges of each square with some of the reserved juice. Fold each square of dough to make a triangle, and crimp the edges with a fork to seal. Move the triangles to the prepared baking sheets, and refrigerate for 15 minutes.

Brush the tops of the turnovers with more of the cherry juice and generously sprinkle the tops with sugar. Bake the turnovers until golden brown (20-25 minutes), rotating the pan halfway through. Move the turnovers off the baking sheet to a wire rack and cool slightly. Serve warm.