Blend the ricotta, mascarpone, egg yolk, and powdered sugar in a food processor until smooth and creamy. Transfer the ricotta mixture to a small bowl, then cover and refrigerate for 30 minutes.
Meanwhile, blend the strawberries and 1 tablespoon of sugar in a clean food processor until smooth. Transfer the strawberry sauce to a small bowl and set aside.
Whisk the chocolate-hazelnut spread and cream in a medium bowl to blend.
Position the oven rack in the center of the oven and preheat to 450 degrees F.
Line a heavy large baking sheet with parchment paper. Roll out each piece of pizza dough into a 7-inch-diameter round. Spoon the ricotta mixture atop the center of the lower half of each pizza dough. Spoon the chocolate-hazelnut mixture atop the cheese mixture. Brush the lower edges of the dough with egg wash. Fold the plain dough halves over the filling, forming half circles. Pinch the edges of dough firmly together to seal. Using a pastry wheel, trim the edges. Transfer the calzones to the prepared baking sheet, spacing evenly.
Brush the tops of the calzones with more egg wash. Bake until the calzones puff and become golden brown, about 10 minutes. Transfer the baking sheet to a rack and cool for 15 minutes. Transfer the calzones to plates and dust with the powdered sugar. Drizzle the strawberry sauce around the calzones and serve.