Heat 1 3/4 cup of the milk in a heatproof measuring cup in the microwave (or a small pan over medium heat) until bubbles form in a ring around the edge. Add the chocolate to the milk and whisk until all chocolate is melted. Set aside.

In a heavy medium saucepan, whisk the stevia, brown sugar, cornstarch, cocoa, and salt with the remaining 1/4 cup cold milk. Cook over medium heat, whisking often, until the mixture is thick enough for your finger to leave a line on coated spoon, about 10-15 minutes. Do not let the mixture boil.

Off the heat, add the reserved chocolate milk and mix until incorporated. Stir in the vanilla. Return the mixture to the heat until it is very thick, about 1 minute. Divide the hot pudding among 5 pudding cups or small bowls. To avoid a skin forming, press plastic wrap onto the surface of each serving. Cool and serve the pudding lukewarm, at room temperature, or refrigerate until chilled, 4 hours, before serving. This recipe keeps for 4 days, covered, in the refrigerator.