Heat the olive oil in a saucepan. Put the cloves of garlic (with skin) in the oil and leave to soften over a very low flame for 15 minutes, making sure the garlic doesn’t burn. Leave to cool in the oil. Place the emulsifying disk in the food processor.
Squeeze the garlic between thumb and index finger into the bowl (discard the skin). Add the egg yolk, mustard, vinegar and a pinch of salt. Mix for 15 seconds. Leave the motor running and add the garlic oil in a trickle through the feeding tube. Stop every now and then to give the yolk a chance to incorporate the oil. When all of the garlic oil has been added, you can add the sunflower oil a little faster. Continue until you get a thick, creamy mayonnaise. Season to taste.
20 minutes total preparation time
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