In a small sauce pot over medium-low heat, combine 2 cups diced strawberries, corn starch, lemon juice, sugar, and vanilla extract. Cook, while stirring, until a sauce has formed, about 5 minutes. Remove from heat and cool. Reserve ¼ cup of the strawberry mixture to make the glaze.
Preheat the oven to 375 degrees. Unroll the pie dough and cut out 4 matching rectangles. In a small bowl mix the egg and water to create an egg-wash. Place an even amount of the strawberry mixture to the center of half of the rectangles, and do not overfill. Leave a clean edge around the dough to seal properly. Place another piece of the cut pie dough on top of the mixture and use the tines of a fork to seal. Transfer the pastries to a parchment lined cookie sheet. Use a pastry brush to apply a thin layer of the egg-wash. Sprinkle each pastry with the remaining sugar. Bake for 7-10 minutes or until golden brown. Remove from oven and let cool to room temperature.
In a small bowl mash the reserved berry mixture with a fork. In another bowl, add in 1 cup confectioners' sugar and a small amount of the strawberry mixture, stir until completely combined. Adjust consistency with more confectioners' sugar or strawberry sauce. Drizzle each tart with the glaze.