In a medium pot, whisk together the apple cider, half and half, sugar, cornstarch, salt, and egg yolks.
Add the pot to the stovetop over medium-low heat.
Cook the pudding, whisking every minute or so, until it is completely bubbling (about 6-8 minutes).
Once it reaches the bubbling stage, cook it another 2-3 minutes, whisking just once or twice, until it is thickened but pourable. Do not over whisk because you could break down the binding action happening in the pudding. Make sure the pudding is still pourable; it will thicken more as it cools.
Remove the pudding from the heat. Whisk in the butter and vanilla extract.
Optional: if you are concerned about any lumps in your pudding, you can strain it into a bowl by pouring it through a fine mesh sieve, pressing the pudding through with a spoon, and discarding what will not pass through.
Pour your pudding either into a bowl or into individual serving dishes. Allow the pudding to cool to lukewarm on the counter.
Once lukewarm, cover your pudding with plastic wrap, lightly pressing the wrap down on the surface of the pudding so it is completely touching and covered by the wrap.
Chill in the fridge for several hours before serving.