Preheat the oven to 425°F. Line a baking sheet with aluminum foil. Place the sweet potatoes on the baking sheet and poke each one several times with a fork. Bake for 50–60 minutes, or until tender.
Let the sweet potatoes cool until they’re easy to handle. Slice them open, peel away the skins, and add the flesh to a food processor, immersion blender, or blender. Purée until completely smooth.
Reduce the oven temperature to 350°F.
In a large mixing bowl, combine the mashed sweet potatoes and butter. Mix until smooth. Add the granulated sugar and brown sugar and stir to combine.
Beat in the eggs, followed by the evaporated milk, vanilla extract, cinnamon, nutmeg, ginger, and salt. Mix until the sweet potato filling is smooth and well combined.
Place the pie crust on a baking sheet. Pour the sweet potato filling into the crust and smooth the top.
Bake for 50–60 minutes, until the center of the pie is mostly set with just a slight jiggle. Remove from the oven and let cool for at least 30 minutes.
Preheat the broiler on high. Spread mini marshmallows evenly over the top of the pie.
Broil for 1–2 minutes, watching closely, until the marshmallows are lightly toasted.
Let the pie cool to room temperature, then refrigerate for 1–2 hours for best slicing.
Notes
Baking the sweet potatoes first is the best way to control moisture and get a smooth filling.
Letting the pie cool fully helps the custard filling set properly.
Store leftover pie covered or in an airtight container in the refrigerator.