Drain the potatoes, put them in a bowl and mash them using a mechanical potato press. To them, gradually add the diced butter (work fast in order to make use of the potatoes' warmth), stir until fully melted.
Now comes the hot milk. Beat with a mixer, pour the hot milk in a trickle, to obtain a smooth and fluffy mixture.
Add the egg yolk but only if you're 100% sure that it's from a fresh egg. If needed, add more salt and beat until the mixture becomes homogeneous.
Making mashed potatoes with a mixer this way yields perfect results.