Bring a saucepan of lightly salted water to a boil. Add the broccoli and cook 1 minute. Drain and rinse under cold water until cool; pat dry. Mix the broccoli, cheddar, sour cream and chives in a bowl until combined, then squeeze the mixture together with your hands to make it compact.
Preheat the oven to 425 degrees F and brush a baking sheet lightly with vegetable oil. On a floured surface, roll out the dough and fill the dinner pockets. (See Cook's Note for step-by-step directions.)
Place the pockets seam-side down on the prepared baking sheet. Beat the egg and 1 tablespoon water in a small bowl; brush the pockets with the egg wash. Bake until golden brown, about 15 minutes.
Photograph by Carrie Purcell
How to Make Dinner Pockets: 1. Cut the dough into 4 pieces. Roll each piece into a 6-by-8-inch rectangle on a floured surface. 2. Put one-quarter of the filling in the center of each dough rectangle, pressing it together. 3. Fold the 2 shorter sides of the dough over the filling, stretching the dough to cover. 4. Fold in the 2 long sides of the dough like a burrito. Pinch the edges to seal.
Recipe courtesy Food Network Magazine