How to Make It
In a small saucepan, combine the milk and sugar and bring to a simmer, whisking constantly, until the sugar dissolves. Cook over very low heat (the mixture should not bubble), stirring occasionally, until thickened and reduced to 1 1/4 cups, about 2 hours and 30 minutes. Stir in the vanilla and scrape the sweetened condensed milk into a medium bowl.
In a food processor, pulse the graham crackers with the brown sugar until fine crumbs form. Add the butter and pulse until incorporated. Press the crumbs evenly over the bottom and up the side of a 9-inch glass pie plate to form a 1/2-inch-thick crust; use the bottom of a metal measuring cup to help form an even layer of crumbs. Refrigerate the crust for at least 45 minutes.
Preheat the oven to 350°. Bake the crust for about 12 minutes, until fragrant and browned. Transfer to a rack and let cool completely.
In a medium bowl, beat the egg yolks. In a medium saucepan, whisk the sweetened condensed milk with the cornstarch until well blended. Add the lemon zest and lemon juice and bring to a simmer. Cook over moderately low heat, whisking, until thickened, 1 to 2 minutes. While whisking constantly, slowly drizzle half of the milk mixture into the egg yolks. Add the egg yolk mixture to the saucepan and cook over moderately low heat, whisking, until very thick, about 3 minutes. Whisk in the butter until smooth. Pour the custard into the crust and let cool to room temperature.
Preheat the oven to 325°. In a medium saucepan, combine the sugar and water and bring to a boil. Cook over moderate heat until the syrup reaches 243° on a candy thermometer, 8 to 10 minutes.
Meanwhile, in the bowl of a stand mixer fitted with the whisk, beat the egg whites with the cream of tartar at medium speed until soft peaks form. With the machine on, slowly drizzle in the hot syrup and beat the meringue at medium-high speed until stiff and glossy, about 10 minutes. Scoop the meringue onto the pie, spreading and swirling it decoratively; make sure the meringue covers the filling completely and touches the crust all around.
Bake the pie on the middle rack of the oven for 10 minutes Turn on the broiler; broil the meringue 6 inches from the heat until golden brown in spots, about 3 minutes (or use a blowtorch). Transfer the pie to a wire rack to cool completely. Refrigerate until chilled, 3 hours.