Preheat your oven to 425°F.
Transfer the pie crust to your pie plate and crimp the edges. Line the crust with parchment paper and fill it with pie weights, beans, or rice to keep it from puffing up.
Bake for 10 minutes. After this time, remove the weights and parchment, then reduce the oven temperature to 375°F.
Return to the oven and bake for an additional 7 minutes, or until the edges are lightly browned.
Reduce the oven temperature to 350°F.
Fill a medium pot with water and add a generous amount of salt. Peel the sweet potatoes and cut them into 1 to 2-inch chunks.
Place the sweet potatoes in the pot and bring the water to a boil. Cook at a low boil until tender, about 15 minutes. Drain well to remove excess moisture.
In a large mixing bowl, beat together the sweet potatoes, butter, brown sugar, molasses, cinnamon, allspice, nutmeg, vanilla extract, and salt. Mix until smooth and creamy.
Add the eggs one at a time, beating well after each addition.
Transfer the filling to the baked pie crust and smooth the top.
Bake for 45 minutes or until the center is set.
If refrigerating: Allow the pie to cool, then cover with plastic wrap and refrigerate for up to 3 days.
When ready to serve: Remove from the refrigerator and let it warm on the counter for 30 minutes before topping with miniature marshmallows and broiling for 1 to 2 minutes until golden brown.
If serving immediately: Cool the pie slightly and top with marshmallows, then broil until the marshmallows are golden brown and toasted.