Step 1

Pulse granulated sugar, salt, and 3 cups flour in a food processor to combine. Add butter and shortening and pulse until mixture resembles coarse meal with a few pea-size pieces of butter remaining. Transfer to a large bowl.

Step 2

Whisk egg yolks, vinegar, and ½ cup ice water in a small bowl. Drizzle half of egg mixture over flour mixture and, using a fork, mix gently just until combined. Add remaining egg mixture and mix until dough just comes together (you will have some unincorporated pieces).

Step 3

Turn out dough onto a lightly floured surface, flatten slightly, and cut into quarters. Stack pieces on top of one another, placing unincorporated dry pieces of dough between layers, and press down to combine. Repeat process twice more (all pieces of dough should be incorporated at this point). Form dough into two 1”-thick disks. Wrap in plastic; chill at least 1 hour.

Step 4

DO AHEAD: Dough can be made 2 days ahead. Keep chilled, or freeze up to 3 months.

Step 5

Toss cranberries, blueberries, raspberries, and sugar in a large bowl. Let stand, tossing occasionally, until berries release their juices, 50–60 minutes.

Step 6

Drain berries in a fine-mesh sieve over a bowl, reserving liquid. Set berries aside. Transfer liquid to a blender, add lemon juice, cornstarch, salt, 3 Tbsp. flour, and ¼ cup berries, purée until smooth. Transfer to a small saucepan and cook over medium heat, stirring constantly, until thickened, about 2 minutes. Transfer purée to a large bowl, stir in lemon zest, orange zest, and reserved berries and toss to combine.

Step 7

Place a rack in lower third of oven and preheat to 375°. Roll out 1 disk of dough on a lightly floured surface into a 14” round. Transfer to a 9” pie dish. Lift up edges and allow dough to slump down into dish. Trim, leaving about 1” overhang. Pour filling into crust and chill in freezer 15 minutes.

Step 8

Meanwhile, roll out remaining disk of dough into a 14” round. Brush edge of dough in pie plate with beaten egg, then place dough round over filling. Trim overhang, fold edge of top crust underneath edge of bottom crust, and press together to seal; crimp edge.

Step 9

Brush top crust with beaten egg and sprinkle edge with raw sugar. Cut vents in top crust. Place pie dish on a rimmed baking sheet and bake 30 minutes. Reduce heat to 350°, rotate pie, and continue baking, tenting with foil if crust is browning too quickly, until juices are bubbling and crust is golden brown, 45–60 minutes longer. Transfer to a wire rack and let cool at least 4 hours before slicing.

Step 10

DO AHEAD: Pie can be baked 2 days ahead. Cover and chill.