Chop the bacon into pieces and place in the frying pan. Cook over a medium heat for 3 to 5 minutes, or until the bacon pieces are crisp and the fat rendered.
Leave the bacon to cool and set aside a few pieces of bacon to garnish.
Peel the garlic and place it in a small saucepan with the oil.
Cook over a low heat for about 15 minutes. Let the oil and garlic cool.
Put the garlic, mustard, pepper, lemon juice, egg yolks and bacon in a small bowl of a food processor. Blend until mostly smooth.
Transfer the mixture into a mixing bowl.
Start whisking and gradually add the cooled oil from the measuring jug in a steady stream, whisking continuously.
Keep adding the oil until the mixture is thick and glossy.
Check the seasoning and add more salt and pepper if required.
Transfer the bacon aioli to a clean bowl and garnish with the reserved bacon pieces before serving.