Melt butter in a medium skillet over medium. Add carrots and shallots. Cook, stirring occasionally, until tender, about 5 minutes. Add garlic, curry paste, and salt. Cook, stirring occasionally, until fragrant, about 2 minutes. Stir in flour; cook, stirring constantly, until vegetables are coated, about 1 minute. Add broth; let mixture come to a boil, stirring constantly. Continue boiling, stirring constantly, until thickened, about 2 minutes. Stir in chicken, peas, and cream. Remove from heat; let cool completely, about 20 minutes.

Unroll 1 of the piecrusts, and fit inside a 9-inch pie plate. Spoon chicken mixture into piecrust in plate. Cut remaining piecrust in half. Cut 1 half into 3 (1 1/2-inch-wide) strips. Cut remaining half into 7 (1/2-inch-wide) strips. Arrange the 1 1/2-inch-wide strips vertically over filling. Weave the 1/2-inch-wide strips perpendicularly into the wider strips to form a lattice pattern. Press ends of lattice strips to edge of bottom piecrust to seal. Trim excess dough; crimp edges.To cook now: Place a baking sheet in oven; preheat oven to 375°F. Brush crust with egg. Place pie on baking sheet; bake in oven until crust is browned and filling is bubbly, about 55 minutes to 1 hour. Let stand 20 minutes before serving.To freeze for later: Wrap entire pie with plastic wrap. Wrap with heavy-duty aluminum foil. Freeze at least 24 hours (up to 1 month).To thaw and cook: Remove pie from freezer; thaw in refrigerator 24 hours. Remove pie from refrigerator, and unwrap. Place a baking sheet in oven; preheat oven to 375°F. Brush crust with egg. Place pie on preheated baking sheet; bake in oven until crust is browned and filling is bubbly, about 1 hour, 15 minutes. Let stand 20 minutes before serving.