Make garlic oil by simmering (confiting) Garlic (4 clove) cloves in a small saucepan with the Olive Oil (1/2 cup) just covering the garlic. Cook for around 45 minutes, and then remove the cooked garlic from the pan. Allow oil to cool.
Using the back of a chef's knife crush the confit garlic into a paste with a generous pinch Salt (to taste) and set aside.
Whisk together Egg (1), Dijon Mustard (1 tablespoon), and Salt (to taste). In a slow, steady stream, add in cooled garlic oil and whisk until the mixture is thick and creamy.
Adjust seasoning to taste. Mix in juice of the Lemon (1/4) and check the thickness- it should be thick enough to run your finger through the back of the spoon to create a line through the sauce. Add in garlic paste.