Preheat the oven to 400 degrees F. Line a sheet tray with parchment paper.
Add the cream cheese and 1 tablespoon of the granulated sugar to a bowl and beat together with a hand mixer until light and spreadable.
In a large bowl, toss together the remaining 1/2 cup granulated sugar, the strawberries, flour, cornstarch, vanilla extract and salt, and set aside for later use.
Lightly dust your work surface with flour. Unroll the puff pastry and roll it out to an 11-by-17-inch rectangle (almost the size of a half sheet tray). Place on the prepared sheet tray and spread the cream cheese down the center of the puff pastry using first a rubber spatula, and then your fingers to evenly spread it out. Spoon the strawberries on top of the cream cheese. Use a knife to cut 1 1/2-inch slits on both sides of the filling, coming within 1/2-inch of the filling. Alternately fold each strip of dough over each other to create a braid. Tuck in the ends and brush the top of the tart with egg wash and sprinkle with the turbinado sugar. Bake until puffed and golden, 25 to 30 minutes.
Cool for 25 minutes before serving. Dust with confectioners' sugar to garnish and slice to serve.