Mix together rhubarb, strawberries, lemon juice, vanilla, sugar, and cornstarch in a medium saucepan. Heat over medium and simmer, stirring occasionally, until rhubarb is tender, about 7-10 minutes. Set aside and let cool.
Preheat oven to 375° and line two baking sheets with parchment paper. Then whisk together egg and 2 tablespoons of water. Set aside.
Start by working with one sheet of puff pastry while the other sheet remains cool in the refrigerator. Unfold the puff pastry onto a lightly floured sheet of parchment. Using a rolling pin, roll pastry into a 10” square. Cut into 4 even squares.
Place a scant (a little less than) ¼ cup of filling into the center of each square. Brush two adjoining edges of each square with egg wash (see picture). Carefully fold each square in half diagonally to form a triangle (some of the filling may squeeze out). Using a fork, crimp the edges to seal the pastries.
Carefully transfer to prepared baking sheet, spacing at least two inches apart. Brush tops with egg wash and sprinkle with sugar.
Repeat with remaining puff pastry sheet, making a total of 8 turnovers. (If you only have one sheet pan, you can bake the first 4 turnovers while you prepare the last 4).
Bake 18-20 minutes or until golden brown and puffed. Let sit for a few minutes then transfer to a cooling rack.