Step 1

Pulse flour, granulated sugar, and salt in a food processor. Add butter and pulse until mixture is the texture of coarse meal with some larger pea-size pieces. Drizzle in 6 Tbsp. ice water and pulse until dough is evenly moistened. It should hold together when squeezed but not be too wet. Add up to 2 Tbsp. more water if needed. Divide dough in half. Form each into a rectangle and wrap tightly in parchment paper or plastic. Chill at least 1 hour.Do ahead: Dough can be made 2 days ahead. Keep chilled.

Step 2

Combine apricots, granulated sugar, wine, salt, and ½ cup water in a medium saucepan; scrape in seeds from vanilla bean and add pod. Bring to a simmer over medium heat, then reduce heat to medium-low and cook, stirring often, until apricots are plump and sticky and sauce is thick, about 10 minutes. Remove pan from heat and stir in blackberries. Chill filling until cool, 45–50 minutes.

Step 3

Preheat oven to 400°. Roll out 1 piece of dough on a lightly floured sheet of parchment to a 12x10" rectangle. Using parchment, transfer to a rimmed baking sheet. Top dough with filling, spreading out in an even layer and leaving a 1" border all the way around the edges. Dot butter evenly over filling. Roll out remaining piece of dough to a 12x10" rectangle. Brush egg on exposed dough around filling, then lay remaining rectangle of dough over. Seal dough by pressing edges together with a fork. Trim ⅛"–¼" off each side with a paring knife. Cut four 3" slits in top of dough. Cover pie and freeze 15 minutes.

Step 4

Uncover pie and brush top with egg. Bake until deep golden brown and crisp, about 40 minutes. Transfer baking sheet to a wire rack and let pie cool before slicing and serving.

Step 5

While the pie is cooling, whisk cream cheese, brown sugar, butter, and salt in a small bowl until smooth. Whisking constantly, add milk a little at time until glaze is thick but still easy to drizzle. Drizzle over pie while still warm.