Combine the sugar, cornstarch, salt, and cocoa in a medium saucepan.

Slowly whisk in the half-and-half and then the egg yolks.

Bring the mixture to a simmer over medium-high heat, whisking constantly.

Reduce the heat to medium and cook, stirring constantly, until thickened, about 2 minutes. Remove from heat.

Stir in the chocolate chips, butter, and vanilla until everything is melted and smooth.

Press plastic wrap directly onto the pudding surface to prevent a skin, and refrigerate until set, about 3 hours.