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1
Combine milk, brown sugar, and cornstarch in a medium saucepan over medium heat. Cook, whisking constantly, until mixture thickens and coats the back of a spoon, about 10 minutes.
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2
Remove about 1/2 cup of the filling mixture and slowly whisk into beaten egg yolks to temper them. Pour mixture back into the pan and bring to a boil. Reduce heat and continue cooking, whisking constantly, until thickened to a pudding-like consistency, about 10 minutes. Remove from heat; stir in butter and vanilla extract until well mixed.
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3
Cover filling and allow to cool completely, stirring occasionally. Place in an ice bath to speed up the cooling, if desired. Pour mixture into pie crust and set aside.
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4
Preheat the oven to 350 degrees F (175 degrees C).
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5
Beat egg whites and cream of tartar together in the bowl of a stand mixer, or using an electric mixer, until soft peaks start to form. Add sugar gradually, continuing to beat until peaks turn stiff and meringue is glossy.
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6
Cover the pie filling with peaks of meringue, making sure to cover all the filling to the edges of the crust.
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7
Bake in the preheated oven until meringue peaks are browned, 10 to 15 minutes. Let cool to room temperature on a wire rack, about 1 hour. Transfer to the fridge to cool completely, about 4 hours.
