Combine corn syrup and cream in a microwave-safe container. Heat in 30-second intervals until boiling. Put chocolate in a bowl and pour hot cream on top. Stir chocolate until smooth, then chill, stirring often, until firm, about 20 minutes.
Meanwhile, line 2 baking sheets with parchment paper. On a lightly floured surface with a lightly floured rolling pin, roll each pastry dough sheet into a 12-in. square. Cut each square into 16 smaller squares and transfer to a baking sheet.
In a bowl, lightly whisk egg and 1 tbsp. water to blend, then brush over pastry squares. Spoon about 1 tsp. chocolate into the center of each square. Fold 1 corner of each square over to meet the opposite corner, forming a triangle. Press edges to seal. Use a 2 1/2-in. round cutter to trim corners of triangle and form a shape that resembles a three-quarter moon. Wrap trays with plastic wrap and freeze at least 1 hour and up to 1 week. (To save space, after 30 minutes of freezing, put pastries in resealable plastic bags in freezer.)
Preheat oven to 400°. Bake pastries, switching pan positions once, until golden brown, about 15 minutes. Let cool 5 minutes. Put sugar in a bowl and turn beignets in sugar to coat. Serve immediately.
Note: Nutritional analysis is per beignet.