Crush the garlic in a pestle and mortar with a little salt and pepper. Transfer to a large mixing bowl and add the egg yolks and mustard.
Whisk the ingredients together with a balloon whisk or electric whisk until just mixed, then gradually trickle in the oil, drop by drop to begin with, until the mixture begins to thicken. Then continue with the oil in a very thin steady stream until about half has been added.
Thin the mayonnaise with a little lemon juice, then continue whisking in the oil very gradually until very thick. Taste and add a little more lemon juice if you like. Cover and chill until required.
Blanche the asparagus and sugar snaps in a saucepan of boiling water for 2 minutes. Drain and allow to cool. Put all of the vegetables into a plastic bag and chill with the aïoli until required.
When ready to serve, spoon the aïoli into a bowl and set on to a large platter. Arrange the vegetables around the bowl and serve.
Note: If the aïoli should 'split' or separate while you are making it, don't panic. Put 1 egg yolk into a separate bowl and then very gradually whisk the split mixture into the new egg yolk until smooth once more.