Make garlic oil by confiting (simmering) Garlic (4 clove) in a small saucepan with the Olive Oil (1/2 cup) just covering the garlic. Simmer for around 45 minutes, and then remove the cooked garlic from the pan. Allow the oil to cool.
Using the back of a chef's knife, crush the confit garlic into a paste with a generous pinch or two of Salt (to taste) and set aside.
While oil is cooling, preheat oven to 400 degrees F (205 degrees C) to get it ready for the potatoes.
Cut Potato (1 kilogram) into even, 1/2-inch pieces.
Place potatoes on a large baking sheet and toss in Olive Oil (to taste) and Salt (to taste) until all potatoes are coated. Bake in preheated oven until soft, about 10-15 minutes.
To make the aioli, whisk together Egg (1), Dijon Mustard (1 tablespoon), and Salt (to taste). In a steady stream add in cooled garlic oil and whisk until mixture is thick and creamy.
Adjust seasoning to taste. Mix in juice of the Lemon (1/4). The sauce should be thick enough to run your finger through the back of the spoon to create a line through the sauce. Add the crushed confit garlic. Cover and chill until ready to serve.
Finely dice 2 stalks of Scallion (2 stalk).
Let potatoes cool slightly, then add to a large bowl. Mix in the homemade aioli, green onions, and Fresh Parsley (1/2 cup).
Season with Salt and Pepper (to taste), garnish with more green onions and serve.