Make the crust: Pulse the flour, sugar and salt in a food processor. Add the butter and pulse into pea-size pieces. Add 1 egg, the lemon juice and 2 tablespoons ice water and pulse until the dough clumps together but has not yet formed a ball, gradually adding up to 1 tablespoon more ice water as needed. Turn out the dough onto a piece of plastic wrap; press into a disk and wrap. Refrigerate until firm, at least 1 hour or overnight.
Make the filling: Melt the butter in a large skillet over medium-high heat. Add the apples, 2 tablespoons sugar and the ginger. Cook, stirring, until just softened, about 5 minutes. Let cool. Toss the blackberries with the remaining 1/3 cup sugar, the cornstarch, vanilla and lemon zest in a large bowl. Add the cooled apples and gently toss to combine.
Preheat the oven to 400 degrees F and line a baking sheet with parchment paper. Roll out the dough into a 12-inch round on a lightly floured surface. Transfer the dough to the prepared baking sheet and refrigerate 10 minutes.
Spoon the fruit mixture onto the dough, leaving a 2-inch border. Fold the edge of the dough over the fruit by about 2 inches, pleating as needed.
Lightly beat the remaining egg with 1 teaspoon water. Brush the dough with the egg wash and sprinkle with sugar. Bake until the crust is golden brown and the filling is bubbling, about 40 minutes. Microwave the jelly in a small heatproof bowl until melted, about 45 seconds. Brush over the fruit. Let cool on the baking sheet.