Set the butter out to soften. You will probably only need one stick. Peel all the potatoes and rinse in cold water. Make sure they are peeled well. You don't want specks of peels in these. That's another recipe.
Cut potatoes into pieces - about 1 inch cubes.
Place cut potatoes in a large stock pot and cover with cold water. Bring to a boil on the stove and cook until potatoes are fork tender. While the potatoes are cooking; you want to get all your other items ready. You need to mix them while they are hot.
While the potatoes are cooking, get out your mixer and set it up. You will need a large bowl and just the regular mixer thingys - nothing fancy. Get the evaporated milk out and open the can. I just use a bottle opener and make 2 openings in it. *Note - the milk needs to be at room temp. Have your spatula ready and the salt and pepper handy. Put a colander in the sink.
When the potatoes are fork tender; drain them in the colander you have waiting in the sink. Now dump the potatoes into the mixing bowl. Add a nice big chunk of butter and pour in some evaporated milk. Enough to get the mixer mixing easily. Mix it at medium speed and switch to a higher speed - adding evaporated milk a little at a time. I like mine to be about the consistency of whipped cream. It won't be fluffy like whipped cream but I can't think of anything else to compare it to.
Add some salt. Quite a bit, actually. You will need to start tasting and keep adding salt until it gets just right. You can add more butter, too. And then the pepper. A little or a lot. I usually like a lot of pepper but in these I just put a little.