Preheat oven to 375 degrees.
Cut the top off of the head of garlic. Place on sheet of heavy aluminum foil. Drizzle olive oil over top, and fold up the foil around the garlic, making a purse.
Roast in the oven for 30 - 40 minutes until garlic is golden and soft. Let cool completely.
In the bowl of a food processor, combine the egg yolks, dijon mustard, lemon juice, salt, champagne vinegar and garlic, squeezing each clove out and into the bowl.
Pulse just combined. Scrape sides of food processor.
With the food processor running, SLOWLY add the oil by small drips until fully emulsified.
Serve along side fries, beef, and fish.
Can be stored in an air-tight container for up to a week in the fridge.