FOR CRUST: Blend flour, sugar and salt in processor for 10 seconds. Add butter and process until mixture resembles coarse meal. Add shortening. Cut shortening into pea-size pieces using on/off turns. Sprinkle ice water over mixture. Process just until moist clumps form, about 5 seconds. Form dough into flat disk. Wrap and chill until cold, about 1 hour. (Can be prepared 1 day ahead)
Roll out dough on lightly floured surface to scant 1/4-inch thickness (about 13-inch round). Fold dough in half and transfer to 9-inch glass pie dish. Unfold and gently press into place. Trim edges leaving 1/2-inch overhang. Form highstanding rim, Freeze crust 20 minutes.
Position rack in center of oven and preheat to 425 degrees F. Line crust with foil and fill with dried beans or pie weights. Bake until crust begins to color. About 25 minutes. Remove beans and foil. Brush crust heavily with beaten egg. Bake until egg glaze is dry and set, about 5 minutes. Maintain oven temperature.
Sprinkle chocolate over hot crust. Let chocolate soften. Spread chocolate over inside of crust. Freeze crust until chocolate is set, about 20 minutes. Sprinkle nuts onto chocolate on crust bottom.
FOR FILLING: Using electric mixer, beat first 4 ingredients until smooth. Add eggs 1 at a time, beating just to blend after each addition. Mix in butter.
Pour filling into crust. Bake until center of pie is loosely set and top is brown, covering edges with foil if browning quickly, about 55 minutes. Cool.
