Make the filling: In a medium saucepan, bring the berries, sugar and ½ cup water to a gentle boil over medium heat and continue to simmer for about 15 minutes. (Some juice should steam off, which concentrates the blueberry flavor.) Mix the cornstarch with about ½ cup water and slowly pour it into the boiling berries, stirring constantly. Continue to stir and boil gently for 1 more minute. Remove from the heat and allow to cool to room temperature, stirring occasionally. Chill completely in the refrigerator.

Make the pastry: In a food processor, blend the flour, salt, and sugar. Add the cold butter cubes and pulse until it looks like a coarse meal with pea-size pieces of butter remaining in the mixture. Add the egg yolk, vanilla, and ice water into the food processor and pulse until a soft, uniform dough forms. Divide the dough into 2 disks, then wrap in plastic wrap and let rest in the refrigerator for 20 minutes.

Roll out the dough: On a well-floured surface, roll each portion of the dough out to about ⅛ inch thick, or roughly a 10-by-15-inch rectangle. (The dough will be sticky, so use a lot of flour on the board and rolling pin.) Cut the dough into 5-inch rounds.

Assemble the stonekes: Whisk the egg and 1 teaspoon cold water together in a small bowl. Brush the edges of each round with the egg wash, then scoop 1 ½-2 tablespoons of the blueberry compote onto the center of each round. Add a few whole berries to each one. Fold the dough over the filling to form a half-moon shaped pastry. Pinch the top closed, then crimp along the edge with the back of a fork. Brush with more egg wash. Cut 3 small slits in the center of each one with a sharp knife to allow the steam to vent. Sprinkle ½ teaspoon demerara sugar atop each pastry. 

Preheat the oven to 400°F. Place the pastries onto a parchment-lined baking sheet and chill in the refrigerator for 20 minutes. Bake the pastries for 10 minutes, then reduce the heat to 375°F and cook for an additional 10-15 minutes, until the pastries are golden brown. Carefully remove and set on a wire rack to cool.