Add the sugar, cocoa powder, and cornstarch to a small sauce pot and stir to combine.
Add the half and half and vanilla extract to the sauce pot. Place the pot over medium heat and begin to whisk everything together. The cocoa will repel the liquid at first, but as the half and half begins to warm, they will come together.
Continue to heat the mixture while whisking until it comes to a gentle simmer, at which point it will thicken into a pudding. Remove the pudding from the heat.
Serve the chocolate pudding warm, or refrigerate until cool. To refrigerate, place a layer or plastic wrap or parchment on the surface of the pudding to prevent a skin from forming on top.
*You can adjust the sugar up or down according to your taste buds, or try a sugar substitute.**You can use any dairy or non-dairy milk in place of the half and half, but keep in mind that the richness of the "milk" determines the richness of the pudding. Half and half is my favorite.