Preheat the oven to 350°F.

To make the crust dough: In a large bowl, stir together the flour, granulated sugar, and salt, mixing well. Add the shortening and, using a pastry blender or a fork, work it into the flour mixture until crumbly and the bits of shortening are the size of peas.

In a medium bowl, whisk together the eggs, water, and vinegar. Add most of the liquid to the flour mixture and stir together with a fork until all the ingredients are evenly moistened and the dough holds together, adding more water if needed. If the mixture is too wet, you can add a little more flour. The dough should hold its shape and be neither tacky nor crumbly and dry. Knead the dough in the bowl to bring it together into a smooth ball.

Lightly flour a large work surface and turn the dough onto it. Divide the dough in half and set half aside, covering it with plastic wrap. Using a floured rolling pin, roll out the other half into a rectangle about 14 by 18 inches and ⅛ to ¼ inch thick. Roll the dough up on the rolling pin, then unfurl it over a 9 by 13-inch baking dish, easing it onto the bottom and up the sides. Trim any excess, leaving a 1-inch overhang. If the dough tears, don't worry about it; just press it back together in the dish.

Flour the work surface again. Take the remaining dough ball, cut it in half, and roll one half into a rectangle about 6 by 15 inches and ⅛ to ¼ inch thick. Cover with a kitchen towel and set aside. Flour the surface again, take the final dough ball, and roll it into a rectangle about 6 by 11 inches and ⅛ to ¼ inch thick. Cover with another kitchen towel and set aside. (For easier handling, transfer the doughs to floured parchment and store them, covered, in the refrigerator, until it is time to cut them and weave the lattice.)

To make the filling: In a medium bowl, combine the blackberries, brown sugar, lemon juice, cornstarch, cinnamon, vanilla, and salt. Stir to mix well.

Pour the filling into the prepared baking dish. Using a chef's knife, cut each reserved sheet of dough, long-ways, into even 1-inch-wide strips. Evenly place the six longest strips across the length of the filling. Evenly weave in the six shorter strips across the width of the filling to form a lattice top. Crimp together the ends of the strips with the bottom crust overhang, trimming off any excess dough. Place the baking dish on a large baking sheet and transfer to the oven.

Bake the cobbler until the filling has thick bubbling in the center and the pastry is light golden brown, about 1 hour. Let the cobbler rest for about 10 minutes before serving.

Leftover cobbler will keep, tightly covered, in the refrigerator for up to 6 days.