In a medium saucepan whisk together sugar, cornstarch, salt, milk, and egg yolks. Cook over medium-low heat, whisking occasionally (every minute or two), until the mixture is bubbling all throughout (this took 7-8 minutes for min).
Once bubbling, continue cooking for one to two additional minutes, whisking once or twice, but not too vigorously (this can break down the binding properties). At this point the pudding should be thickened but still pourable, it will thicken more as it cools.
Remove from heat and whisk in butter and vanilla extract.
Place a fine mesh strainer over a large heatproof bowl. Pour the mixture through the strainer and into the bowl. Skip this step if you don't notice any lumps in your pudding.
Transfer the pudding into a large bowl or into individual serving bowls. Cool until it is lukewarm, then cover with plastic wrap. Refrigerate for several hours or until chilled.