Preheat oven to 375 degrees F (190 degrees C). Spray bottom and sides of a 9x13-inch baking pan with cooking spray.

Combine chicken, Mexican cheese blend, mayonnaise, broccoli, onion, red bell pepper, garlic, almonds, and dill in a large bowl.

Roll pastry sheets on a floured surface until all sides measure 3 inches longer than the bottom of the prepared pan. Place 1 sheet on the bottom of the pan and against the sides. Pour the chicken filling evenly over the bottom crust. Top with the second crust, folding the ends between the pan and the bottom crust. Pinch crusts together to seal.

Beat egg with water and salt in a bowl; brush mixture over the top crust. Cut vents into the top for steam to escape.

Bake in the preheated oven until golden brown on top, about 30 minutes.