I like Jamie Oliver's aioli recipe - and it is quick and easy to make. I've also tried a recipe (not sure, but think it was Anton Edelman's recipe) which used oven baked garlic, which was allowed to cool before starting the process.
1/2 small clove of garlic, peeled
1 teaspoon salt
1 large egg yolk
1 teaspoon Dijon mustard
approx. 285ml/1/2 pint extra virgin olive oil
approx. 285ml/1/2 pint olive oil
lemon juice, to taste
When I make aioli I use two olive oils: one that is a bit more expensive, a bit more peppery and a bit more gutsy; and a second which is a bit more bland but still nice and mellow. By blending the flavours in this way you achieve an olive oil flavour that isn't too strong or too peppery. Aioli is great with cold roast pork. Basil aioli is good with pink grilled salmon and lemon aioli works well with crostini in fish broth.
Smash up the garlic with 1 teaspoon of salt in a pestle and mortar (if you don't have a pestle and mortar you can very finely chop the garlic). Place the egg yolk and mustard in a bowl and whisk. Then start to add your olive oil bit by bit. Once you've blended in a quarter of the olive oil you can start to add the rest in larger amounts. When you've added it all, you can add the garlic and lemon (to taste) and any extra flavours such as basil, fennel tops, dill, chopped roast nuts. To finish just season to taste with salt, freshly ground black pepper and lemon juice.