Place sausage links on a microwave-safe plate lined with a paper towel. Microwave at 50% power for 1 to 1 1/2 minutes.
Preheat the oven to 400 degrees F. Press one pie pastry into an ungreased 9-inch pie plate; set remaining pastry aside. Whisk one egg in a small bowl for egg wash.
Whisk remaining 5 eggs together in a bowl. Cut sausage into small pieces; add to eggs along with mixed vegetables, cheese, salt, and pepper. Stir until well combined, then pour into bottom pastry. Place remaining pastry over top and crimp the edges to seal. Cut 3 slits in top pastry and brush with egg wash.
Bake in the preheated oven until the internal temperature reaches 165 degrees F (74 degrees C), 35 to 37 minutes. Cover pie with foil if needed to prevent top crust from getting too brown. Let stand for 10 minutes before cutting and serving.