Whisk the 4 cups pastry flour with 3/4 teaspoon salt. Cut in the cold pastry butter until pea-size pieces remain, then toss in 1/2 cup ice water and only enough extra water to make a dough that holds when pressed. Divide into three discs, wrap and refrigerate for 45 minutes.
Heat oil in a skillet over medium-high heat. Cook chicken for 6 to 8 minutes, stirring, until 165°F; add broccoli and corn and cook for 4 minutes until the broccoli softens, then transfer to a bowl.
Melt filling butter in the skillet and stir in filling flour for 1 minute. Gradually whisk in broth and milk and simmer for 3 minutes until thick; remove from heat, add cheddar, pepper and remaining salt and fold in chicken and vegetables.
Spread filling in a shallow dish and refrigerate promptly for 30 minutes until cold. Heat oven to 400°F and line two sheet pans with parchment.
Roll dough on the measured rolling flour to about 1/8 inch thick. Cut twelve 6-inch rounds, gently rerolling scraps once; divide all filling evenly among one half of each round, leaving a 1/2-inch border.
Brush borders with a little egg wash, fold into half-moons and press seams firmly with a fork. Transfer to pans, brush tops with remaining egg wash and cut one short steam slit in each.
Bake for 28 to 32 minutes, rotating pans halfway, until deeply golden and the filling reaches 165°F. Cool on racks and refrigerate within 2 hours, then freeze chilled pies individually on a tray and bag for up to 2 months.
For one serving, microwave two frozen pies on a microwave-safe plate at 50 percent power for 3 minutes, then in 30-second bursts at full power until both centers reach 165°F. Transfer to a 375°F oven for 6 to 8 minutes to crisp, then rest for 3 minutes before eating.