In a medium saucepan, whisk together the brown sugar, cornstarch, and salt. Slowly add the milk, whisking constantly to prevent lumps. Cook over medium heat, stirring frequently, until the mixture thickens and begins to bubble—about 5 to 7 minutes.

In a separate bowl, whisk the egg yolks. Gradually pour about 1/2 cup of the hot mixture into the yolks, whisking constantly to temper the eggs. Pour the tempered egg mixture back into the saucepan and continue cooking for another 2 to 3 minutes, stirring constantly, until thick and smooth.

Remove the pan from heat and stir in the butter and vanilla extract until fully incorporated. Pour the butterscotch filling into the prepared pie crust, spreading it evenly. Cover with plastic wrap, pressing the wrap directly onto the surface to prevent a skin from forming. Chill in the refrigerator for at least 4 hours, or until fully set.

Preheat your oven to 350°F (175°C). In a clean bowl, beat the egg whites and cream of tartar until soft peaks form. Gradually add the granulated sugar, beating until stiff, glossy peaks form. Spread the meringue over the chilled filling, making sure to seal the edges to the crust.

Bake the pie for 10 to 12 minutes, or until the meringue is golden brown. Let cool completely before serving. Top with whipped cream and extra butterscotch chips or a drizzle of caramel sauce if desired.