Preheat oven to 200°C / 400°F. Pierce sweet potatoes with a fork. Roast on a foil-lined baking sheet for 45 to 55 minutes until completely tender and caramelized. Cool 20 minutes, peel, and mash until smooth.
Reduce oven to 190°C / 375°F. Fit pie crust into a deep-dish 9-inch pie dish. Line with parchment and fill with pie weights. Blind bake 15 minutes, remove weights and parchment, bake 5 more minutes until pale gold. Remove from oven.
Reduce oven to 175°C / 350°F.
Beat 2 cups (450g) of mashed sweet potato with melted butter until completely smooth. Add both sugars and beat until combined. Add eggs and yolk one at a time, beating after each. Add evaporated milk, vanilla, cinnamon, nutmeg, ginger, allspice, and salt. Mix until fully combined.
Press filling through a fine-mesh sieve into a large measuring jug to remove fibers and ensure a silky texture.
Place the blind-baked crust on a rimmed baking sheet. Pour filling into the crust. Bake at 175°C / 350°F for 50 to 60 minutes, until edges are set and center has a slight jiggle.
Cool at room temperature 2 hours, then refrigerate at least 2 more hours before slicing. Overnight refrigeration gives the best results.
Serve at room temperature with freshly whipped cream.