Bring a large pot of lightly salted water to a boil over high heat. Add the sweet potatoes and reduce the heat to medium. Cook until the sweet potatoes are tender when pierced with a knife, about 30 minutes. Drain and run under cold water until cool enough to handle. Peel the sweet potatoes and place in a medium bowl.
Mash with an electric mixer on medium speed until very smooth. Measure 3 cups mashed sweet potatoes.
in a medium bowl, using an electric mixer on low speed, mix the mashed sweet potatoes, the remaining melted butter and brown sugar, the granulated sugar, eggs, half-and-half, vanilla, cinnamon, and nutmeg. Spread into the pie shell, smoothing the top.
Set the oven temperature to 350°F. Bake until a knife inserted in the center of the filling comes out clean, about 1 ½ hours. Cool completely on a wire cake rack. Cover and refrigerate until ready to serve with whipped cream.