Instructions

for the crust

Combine ½ cup chilled sour cream and 1 lightly beaten egg in bowl. Cut 12 tablespoons chilled unsalted butter into ½-inch pieces.
Process 12½ ounces all-purpose flour and 1½ teaspoons table salt in food processor until combined, about 3 seconds. Add butter and pulse until only pea-size pieces remain, about 10 pulses.
Add half of sour cream mixture and pulse until combined, 5 pulses. Add remaining sour cream mixture and pulse until dough begins to form, about 10 pulses.
Transfer mixture to lightly floured counter and knead briefly until dough comes together. Divide dough in half and form each half into 4-inch disk. Wrap disks tightly in plastic wrap and refrigerate for 1 hour.
Let chilled dough sit on counter to soften slightly, about 10 minutes, before rolling. Roll 1 disk of dough into 12-inch circle on lightly floured counter.
Loosely roll dough around rolling pin and gently unroll it onto 9-inch pie plate, letting excess dough hang over edge. Ease dough into plate by gently lifting edge of dough with your hand while pressing into plate bottom with your other hand.
Roll other disk of dough into 12-inch circle on lightly floured counter, then transfer to parchment paper–lined baking sheet; cover with plastic. Refrigerate both doughs for 30 minutes.

for the filling

Meanwhile, adjust oven rack to lowest position and heat oven to 450 degrees. Melt 4 tablespoons unsalted butter in large saucepan over medium heat. Add 1 finely chopped onion, 2 carrots, peeled, and cut into ¼-inch pieces, 2 celery ribs cut into ¼-inch pieces, ½ teaspoon salt, and ½ teaspoon pepper and cook until vegetables begin to soften, about 6 minutes.
Add 6 tablespoons all-purpose flour and cook, stirring constantly, until golden, 1 to 2 minutes. Slowly stir in 2¼ cups chicken broth and ½ cup half-and-half and bring to boil over medium-high heat. Stir in 1 russet potato, peeled, and cut into ¼-inch pieces and 1 teaspoon minced thyme.
Reduce heat to medium and simmer until sauce is thickened and potato is tender, about 8 minutes. Off heat, stir in 3 cups shredded rotisserie chicken meat and ¾ cup frozen peas.
Transfer filling to dough-lined pie plate. Loosely roll remaining dough round around rolling pin and gently unroll it onto filling.
Trim overhang to ½ inch beyond lip of plate. Pinch edges of top and bottom crusts firmly together. Tuck overhang under itself; folded edge should be flush with edge of plate.
Crimp dough evenly around edge of plate using your fingers. Cut four 2-inch slits in top of dough.
Brush top of pie with 1 lightly beaten large egg. Place pie on rimmed baking sheet. Bake until top is light golden brown, 18 to 20 minutes.
Reduce oven temperature to 375 degrees, rotate sheet, and continue to bake until crust is deep golden brown, 12 to 15 minutes longer.
Let pie cool on wire rack for at least 45 minutes. Serve.TO MAKE AHEAD: At end of step 10, transfer filling to bowl and refrigerate until fully chilled, about 1½ hours. Continue with step 7, then wrap pie tightly in plastic wrap and then aluminum foil. Freeze for up to 1 month. When ready to bake, unwrap frozen pie, cover with foil, and place on rimmed baking sheet (do not thaw). Place sheet on middle rack of cold oven and set oven to 375 degrees. Bake for 1¼ hours. Uncover pie and brush with egg. Rotate sheet and continue to bake until crust is golden brown and filling is beginning to bubble up through slits and registers at least 150 degrees, 55 minutes to 1¼ hours longer. Let cool for 45 minutes before serving.