Combine sugar, milk, butter, lemon juice, egg yolks, cornstarch, and lemon zest in a medium saucepan. Cook over medium heat, stirring constantly, until thick, 15 to 20 minutes. Remove from heat, cover, and let cool, about 30 minutes.
Fold in sour cream; pour into the baked pie crust. Chill in the refrigerator for at least 2 hours.
Beat egg whites, sugar, and cornstarch together in a bowl using an electric mixer until stiff peaks form. Spread meringue on top of filling, right up to the edge of the crust.
Set an oven rack about 6 inches from the heat source and preheat the oven’s broiler.
Broil in the preheated oven until meringue is lightly browned, 5 to 7 minutes. Serve immediately.
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