Preheat the oven to 325 degrees F.
Make the Filling: In a large saucepan, combine the milk and cream and bring to a simmer over medium heat. Immediately remove from the heat and set aside.
Melt the butter in a large, heavy skillet over medium-high heat. Stir in the brown sugar, raise the heat to medium-high, and cook, stirring constantly, until caramelized, 5 to 7 minutes. (You'll smell a characteristic nutty caramel odor when the butter browns, signaling that the mixture is ready.)
Whisking constantly, gradually add the butter/brown sugar mixture to the hot milk/cream mixture. If the mixture isn't smooth, blend for 20 seconds with a hand blender or pour through a fine sieve.
Put the egg yolks in a medium bowl. Whisk in about 1/2 cup of the hot milk mixture. Whisk in the cornstarch and salt until dissolved. Whisk the cornstarch mixture back into the hot milk mixture in the saucepan. Whisk in the Scotch.
While whisking constantly, cook over medium-high heat until thick and just boiling. When the mixture thickens, the whisk will leave trail marks on the bottom of the pot and the mixture will have a few large bubbles boiling up to the top.
Turn off the heat and whisk in the vanilla extract. Pour into the prebaked pie shell and set aside while you make the meringue.
Make the Meringue: In a standing mixer fitted with a whip attachment, whip the whites in a clean dry bowl on low speed until foamy. Add the cream of tartar and continue whipping on medium speed until soft peaks are formed. Gradually pour in the sugar and continue whipping on high speed until stiff and glossy. Pile the meringue onto the pie and swirl to cover, spreading it to the edge. (Making sure it touches the edge.) Bake the pie until the meringue is lightly browned, about 15 to 20 minutes.
Chill the pie, uncovered, at least 2 hours or overnight before serving.
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