Whisk sugar, cocoa, cornstarch, and salt in a saucepan. Gradually add milk, whisking smooth. Cook over medium heat, stirring constantly, until thick and bubbling (about 7–10 minutes).
Lightly beat yolks in a bowl. Slowly whisk in 1 cup of the hot mixture. Pour it back into the pan and cook for 2 more minutes, stirring constantly.
Remove from heat. Stir in butter and vanilla until smooth. Pour filling into pre-baked crust and smooth the top.
Beat egg whites with cream of tartar until soft peaks form. Gradually add sugar, beating to stiff, glossy peaks. Mix in vanilla.
Spread meringue over hot filling, sealing to the crust. Create peaks with a spoon. Broil 1–2 minutes until golden—watch closely.
Cool at room temp for 1–2 hours. Chill at least 3 hours before slicing for a clean cut.