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