I cleaned and cut the potatoes (about 1lb), cover with salted water and hard boil for probably 10ish minutes. (However long it takes me to dice ham and cut green beans). Diced up ham (about 1.5lb) and cut fresh green beans (1 lb bag of fresh) and threw that in for another 15ish min with another pinch of salt. When the potatoes are fork tender it’s just about done.
You can’t overcook this. The longer you cook it, the more flavor the water has and the more the potatoes will break down. You want the water to reduce down a little. But it should still be able to stir. Lower heat to medium low and add a stick of butter an a cup or two of milk. You want it thin but only slightly white in color. Salt and lots of pepper.