In a bowl, mix chicken with Swiss cheese, red pepper, onion and pepper.
In a 1 1/2-2 quart saucepan, mix broth with cornstarch; add cream cheese, whisk over high heat until mixture is boiling (it will be very thick), 2 to 3 minutes; scrape over chicken mixture and combine well, adding salt to taste.
On a lightly floured board, unroll the pizza crust dough; cut each rectangle crosswise into thirds; on one end of each piece, mound about 5 tablespoons chicken mixture; fold the other end of dough over filling to form a rectangle, then fold edges together and pinch to seal.
Gently place empanadas, slightly apart, on a greased 12 by 15-inch baking sheet; in a small bowl, beat egg to blend; brush generously over each pastry.
Bake in a 375° oven until richly browned, about 22 to 25 minutes; transfer to a rack and let cool at least 10 minutes.