Fun fact, the English name is a translation error from 'frijoles refritos,' which is closer to "well fried" in meaning.
I thought it was odd to stipulate the use of a frying pan; I thought the "refritos" bit was a misnomer. My method involves simmering the beans with garlic until soft, mixing in butter, and then whizzing/mashing. There is no "frying" step, unless you like to scour frying pans.
What about rerefried beans? If twice is good, three times must be better?