First place the garlic and olive oil in a small saucepan over the gentlest heat possible - a heat diffuser is good for this - and leave for 1 hour for the garlic to infuse and become really soft.
Use a potato peeler to pare off the skins as thinly as possible and then cut the potatoes into even-sized chunks, not too small. If they are large, quarter them and if they are small, halve them.
Put the potato chunks in a large saucepan, then pour boiling water over them, add 1 dessertspoon of salt, put on a lid and simmer gently until they are absolutely tender - they should take approximately 25 minutes. The way to tell whether they are ready is to pierce them with a skewer in the thickest part; the potato should not be hard in the centre. And you need to be careful here, because if they are slightly underdone you do get lumps.
When the potatoes are cooked, drain them. Cover them with a clean tea cloth to absorb some of the steam for about 5 minutes, then using an electric whisk on a low speed, begin to break them up using half the garlic and oil. As soon as all that is incorporated, add the rest of the garlic and oil and whisk until smooth, seasoning well with salt and freshly milled black pepper.
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