Step 1 Place the flour, one-half teaspoon salt and the zest of one lemon in a food processor and pulse to combine. Cut three-fourths cup (1 1/2 sticks) of the butter into 1-inch cubes and add to the flour. Pulse to break up. Whisk together the vinegar and egg yolk in a measuring cup with enough ice-cold water to bring the volume up to one-half cup. While pulsing, add the liquid in a steady stream until the flour looks crumbly and damp (be careful that the dough does not overmix and form a ball). The crumbs should adhere when you press them together. Turn out the dough onto plastic wrap and press into 1 disk. Wrap tightly in the plastic and refrigerate 30 minutes to an hour.
Step 2 On a lightly floured surface, roll the dough to a large round no thicker than one-eighth inch and about 15 inches in diameter. Drape the dough over the pie plate. Trim the dough to about 2 inches from the rim of the pie plate, saving the trimmings for decoration. Roll up the dough to form a thick crust around the rim of the plate, and crimp the crust to form a zig-zag design. Take the trimmings (ball up the dough and roll it out again if necessary) and cut out about 5 big leaves (or other shapes, such as a pear). Place the leaves on a parchment-covered cookie sheet and, using the flat side of a knife, press veins into the leaves for decoration. Use the remaining dough to make decorative balls for the top of the pie: roll 6 to 8 larger balls the size of small marbles to dot the center over the filling, and about a dozen slightly smaller balls to garnish the rim of the pie along the crust (moisten the smaller balls with a little water so they adhere to the crust). Refrigerate both the pie shell and the decorative dough shapes until ready to fill.
Step 3In a large bowl, toss the remaining lemon zest, one-half cup sugar, the brown sugar, tapioca, cardamom, pepper, nutmeg and remaining one-eighth teaspoon salt to combine. Toss in the pears and lemon juice, then gently fold in the frozen blackberries just until combined.
Step 4Fill the chilled pie shell with the pear-blackberry mixture, dot with the remaining 2 tablespoons butter, then position the dough leaves around the center of the pie and dot the center with the larger balls. (Or decorate how you like.) Refrigerate the pie, uncovered, for 15 minutes. Meanwhile, heat the oven to 400 degrees.
Step 5In a small bowl, whisk together the egg white with the 1 tablespoon water to form an egg wash. Brush both the decorations and crust with egg wash, then sprinkle the decorations with the remaining tablespoon of sugar. Put the pie into the center of a hot oven, placing a cookie sheet on the rack underneath. Bake for 30 minutes. Lower the oven temperature to 350 and bake for about 45 minutes longer, until the crust is golden and the filling is bubbly. Cool on a rack.