Place the sweet potatoes in a pot of salted cold water. Bring to a boil and let boil for 5-10 minutes or until very tender. Drain the sweet potatoes and place them in the bowl of a food processor fitted with the steel blade. Puree until smooth. Add the brown sugar, eggs, half-and-half, melted butter, vanilla, cinnamon, and nutmeg. Process until fully combined, scraping down the sides of the bowl once or twice.
Pour the mixture into the pie crust and bake for 45 minutes or until the filling looks set. Let the pie cool, then refrigerate until cold, about 2 hours.
Preheat the broiler to high and position an oven rack in the top third of the oven.
Beat the egg whites on high speed until frothy. Gradually add the sugar while beating and whip until stiff peaks form. Top the chilled pie with the meringue, spreading it all the way to the edges. With a spatula or back of a spoon, make swirls in the meringue.
Broil, turning once, for 60-90 seconds or until the meringue starts to brown.