For a very pronounced garlic flavor, peel and chop 1 or 2 cloves garlic and reserve. For a milder flavor, leave the garlic cloves unpeeled in their skins and place in a small skillet over medium low heat. Cover and cook, turning once or twice, until softened, about 20 minutes. Cut the root end off the clove, slip the garlic from the skins, and chop.
Add the egg, egg yolk, lemon juice, Dijon mustard, salt and chopped garlic in the bowl of a food processor or blender container. Process for 30 seconds to blend.
Combine the olive oil and room temperature bacon fat in a measuring cup. Turn on the food processor or blender, and very slowly pour a thin stream of the the oil mixture in, letting it slowly incorporate.
When all the fat has been incorporated and the aioli is thick and creamy, taste for seasoning and add additional salt if needed.
If not using right away, transfer to a sealed container and store in the refrigerator for up to three days.
