Pureed dates add complexity to the sticky-sweet filling for this otherwise traditional pecan pie.
On a lightly floured piece of parchment, roll out dough into a 13-inch round, about 1/8 inch thick. Fit into a 9-inch pie dish. Using kitchen shears, trim to a 1-inch overhang; fold under. Crimp edges or decorate as desired. Lightly prick bottom of dough with a fork. Refrigerate 30 minutes.
Preheat oven to 375 degrees with a rack in lower third. Line dough with parchment; fill with dried beans or rice. Bake until edges begin to turn golden, 20 to 25 minutes. Remove beans or rice and parchment; bake until bottom and sides are golden brown, about 20 minutes more. Transfer to a wire rack; let cool completely. (Crust can be made up to a day in advance and covered tightly in foil.)
Reduce oven temperature to 350 degrees. Spread pecans on a rimmed baking sheet and toast until golden and fragrant, 10 to 12 minutes. Let cool completely. Reserve 1 cup for topping; coarsely chop remaining 1 1/2 cups.
In a small saucepan, bring dates, 1/2 cup water, and vanilla to a simmer over medium-high heat. Reduce heat to low; cook until almost all of liquid is absorbed, 7 to 9 minutes. Transfer dates and remaining liquid to a food processor; puree until smooth.
In a large bowl, whisk together eggs, 3/4 cup date puree (reserve remainder for another use), corn syrup, brown sugar, butter, and salt until smooth; stir in chopped pecans. Pour filling into crust; arrange reserved whole pecans over top. Place a foil-lined baking sheet below rack, then place pie dish directly on rack; bake until filling wobbles slightly in center when gently shaken, 50 minutes to 1 hour. (If crust is getting too dark, cover with a foil ring.) Transfer to wire rack; let cool completely, at least 4 hours. Serve room temperature.