For pastry: Combine flour and salt in a large bowl. Cut in butter and shortening until mixture resembles coarse meal. Beat 2 tblsps ice water, egg and vinegar to blend. Mix into flour just until dough comes together into a ball. If dough seems too dry, add up to 2 tblsps more water, a few drops at a time. Wrap in plastic wrap and chill for 1 hour.
For filling: Melt 4 tblsps butter in small skillet over low heat. Add onion, cover and cook gently until soft, stirring occasionally, about 10 minutes. Remove from skillet.
Melt remaining 3 tblsps butter in same skillet over low heat. Add carrots, increase heat to high and stir 2 minutes. Reduce heat to low. Add water, cover and cook until carrots are tender and liquid is absorbed, about 20 minutes (if carrots are tender and there is still liquid, drain).
Puree onions and carrots in processor with eggs, yolks, salt, allspice and pepper until smooth. Turn into bowl and refrigerate 1 hour.
To assemble: Preheat oven to 340°F Grease 5 ½ x 9 ½ inch loaf pan (or 4 ½ x 11 inches).
Roll dough out on lightly-floured surface to thickness of ¼ inch. Cut out 12 x 16 inch rectangle. Drape dough loosely in pan. Press into corners gently with fingers. Trim dough flush with top of pan. Roll scraps out to ¼ inch thick. Cut out rectangle large enough to cover top of pan.
Stir rice and cheese into carrot mixture. Spoon into prepared pan. Brush edge of crust with glaze. Cover with dough, pressing to seal. Roll remaining scraps out. Cut out dough decorations and stick them on with the egg glaze. Brush entire pie with glaze. Make 6 steam vents. Bake until lightly-browned, about 1 ½ hours. Cool in pan. Remove carefully. Serve at room temperature.