Preheat oven to 450 degrees. Place pie crust in a 9-inch pie pan and gently press into the bottom and up the sides. Fold edges under and crimp edges.
Top piecrust with a piece of parchment paper and add pie weights or dried beans. Bake for 10 minutes. Remove the parchment paper and weights and bake another 5 minutes. Let cool.
Reduce oven temperature to 350 degrees.
In a large heavy saucepan, combine brown sugar, 1/4 cup sugar, cornstarch, and salt. Whisk in half-and-half and bring to a boil over medium heat, stirring constantly.
Cook and stir for 2 minutes. Remove from heat.
Place egg yolks in a medium bowl and gradually whisk in 1/4 of the hot half-and-half mixture. This will temper the eggs so that they do not curdle.
Add the egg yolk mixture to the saucepan and whisk in. Cook, whisking continuously, until thick and bubbly, about 3 minutes.
Remove from heat and stir in vanilla and butter until the butter completely melts. Pour into prepared pie crust. Cover with plastic wrap.
In the bowl of an electric mixer, beat egg whites and cream of tartar on high speed until foamy.
Gradually beat in 6 tablespoons of sugar and keep beating until stiff peaks form.
Remove plastic from pie and spoon meringue over filling. Spread it all the way to the edges so that it completely covers and seals the filling.
Bake until golden, about 12 minutes, in in 350 degree oven.
Let cool completely before slicing.