Preheat oven to 375°F (190°C).

Let Vinegar Pie Dough stand at room temperature until slightly softened, about 10 minutes. On a lightly floured surface, roll dough into a 12-inch circle. Transfer to a 9-inch pie plate, pressing into bottom and up sides. Fold edges under, and crimp, if desired. Top with a piece of parchment paper, letting ends extend over edges of plate; add pie weights. Place on a rimmed baking sheet.

Bake for 15 minutes. Carefully remove parchment and weights. Let cool on a wire rack for 20 minutes. Reduce oven temperature to 350°F (180°C).

For filling: In the work bowl of a food processor, place sweet potato; process until smooth. Transfer sweet potato to a medium bowl. Add granulated sugar, melted butter, evaporated milk, eggs, lemon zest, pie spice, vanilla, and salt, whisking until combined. Pour into prepared crust.

For egg wash: In a small bowl, whisk together egg and 1 teaspoon (5 grams) water. Brush egg wash onto crust.

Bake in the lower third of the oven until filling is set, about 40 to 50 minutes, covering crust with foil to prevent excess browning, if necessary. Leave oven on.

For topping: In a medium bowl, stir together pecans, brown sugar, flour, melted butter, pie spice, and salt with a fork until moistened. Sprinkle topping on pie, leaving a 1-inch border.

Bake until pecans are lightly toasted, about 10 minutes, covering crust with foil to prevent excess browning, if necessary. Let cool completely on a wire rack. Drizzle with cane syrup before serving.