Place a rack in the middle position, and preheat oven to 400f (205c).
Take a whole bulb of garlic, and cut the top off the garlic, about 1/4 inch.
Place the garlic bulb on a parchment-lined baking sheet, and drizzle some extra virgin olive oil over the top of the garlic.
Wrap the parchment paper around the garlic bulb, and twist to seal.
Place into the preheated oven, and bake for 30 to 35 minutes. The cloves should be soft.
Remove three of the cloves, and extract from the skin.
Save the additional garlic for another use… Like spreading on toast… YUM.
Add egg yolk, lemon juice, vinegar, mustard, salt, black pepper, and baked garlic to a food processor, fitted with an S-blade.
Blend at high speed, until the color of the mix is bright yellow, about 1 minute.
With the blender set to high speed, very slowly (drop by drop) add the oil, until the mayonnaise is thick, about 8 minutes.
Chef's Tip: Do not rush the adding of the oil, if you add it too fast, it won't emulsify properly.
Cover and chill.
Chef’s Note: Fresh aioli tastes wonderful, and you're not going to miss all those preservatives one tiny bit; however, what you gain in health and taste, you lose in shelf life. You can make this aioli up to two days before use… no more.