Place the sweet potatoes into a large pot and cover with water. Bring to a boil over high heat, then reduce heat to medium-low, cover, and simmer until tender, about 20 minutes.
Drain and allow to steam dry for a minute or two.
Transfer the sweet potatoes into a mixing bowl, and allow to cool for about 10 minutes.
Preheat oven to 350 degrees F (175 degrees C). Line a 9-inch pie dish with unbaked pie crust.
Mash the sweet potatoes smoothly, and mix in butter, 3/4 cup of sugar, salt, milk, egg yolks, cinnamon, and vanilla extract.
Pour the filling into the pie crust.
Bake in the preheated oven until the filling is set and the pie crust is beginning to brown, 25 to 30 minutes.
Place the egg whites into a clean mixing bowl, and beat until stiff with an electric mixer set on medium, 3 to 5 minutes. Beat in 1/4 cup sugar and 1/2 teaspoon of vanilla extract, until the mixture holds firm peaks and is glossy.
Remove the pie from the oven and spoon meringue over the sweet potato filling, swirling the meringue into attractive peaks. Return to oven, and bake until the meringue turns golden brown, about 10 minutes, watching carefully to avoid burning. Allow to cool before serving.
