Preheat oven to 400 degrees F (200 degrees C). Set rack to center of the oven and place a cookie sheet on baking rack.
Whip sweet potatoes in a mixing bowl with an electric hand mixer until soft. Add sweetened condensed milk, eggs, butter, and vanilla extract; continue blending until incorporated. Blend flour, white sugar, brown sugar, cornstarch, cinnamon, nutmeg, baking powder, and salt into the sweet potato mixture.
Divide sweet potato mixture between the pie shells. Cover pies with aluminum foil.
Bake in preheated oven for 10 minutes.
Reduce heat to 300 degrees F (150 degrees C). Continue baking pies uncovered until a toothpick inserted into the center comes out clean, about 40 more minutes.
Remove aluminum foil and pile marshmallows into the center of each pie. Return to oven and continue baking until marshmallows are golden brown, about 10 minutes. Allow pies to cool before serving.