Wet a tea towel and wring out the surplus moisture. Fold it and put it on the work surface to anchor the bowl in which you make the mayonnaise.
Mash the garlic with coarse salt, using the flat side of a knife blade, working it hard against the chopping board until it has emulsified.
Add it to the egg yolks in a bowl, or a mortar, and combine with a small hand-held whisk or, if you prefer, a pestle. Gradually add the oil, drop by drop to begin with, as if you were making mayonnaise, stirring all the time.
Gradually incorporate all the oil, adding a little water and perhaps a few drops of lemon juice (not authentic!) when it gets very stiff. Taste and add more salt and pepper if necesssary.