Preheat oven to 350 degrees with rack on lowest shelf. Make crust: In a food processor, pulse graham crackers, sugar, ginger, and salt until finely ground. Add butter; pulse until mixture forms large, moist crumbs. Press crust into bottom and up sides of a 9-inch pie plate.
Make filling: In a large bowl, whisk together eggs and sugar until combined. Add sweet-potato puree, half-and-half, lemon juice, vanilla, salt, and allspice; whisk until completely smooth. Pour filling into crust; smooth top with a rubber spatula.
Place pie on a baking sheet, and bake until filling is set, 40 to 50 minutes. Transfer pie to a wire rack to cool completely, about 2 hours.
A press-in graham-cracker crust is simple to make (or buy one premade). We added ginger to complement the flavor of the sweet potatoes.