Mix the cocoa powder and sugar together in a small saucepan. Stir the 1 1/2 cups milk into the saucepan until the sugar has dissolved. Place over low heat; slowly bring the mixture to a low simmer.

Whisk 2 tablespoons of milk together with the cornstarch in a small cup; slowly whisk the cornstarch slurry into the cocoa mixture. Continue cooking, whisking continually, until the hot chocolate reaches a pudding-like thickness, 2 to 3 minutes.