Cook the potatoes, barely covered in salted water, until soft. Put through a sieve with the cooking water. Meanwhile, prepare the mussels by scrubbing, scraping and trimming. Cook the garlic in the oil for a few minutes. Add the mussels and cook, covered, over a high flame. As soon as the shells open (discard any that don’t) remove from the pan. Scoop the mussels from the shells.