Cut the potatoes in quarters and place in a large pot, add the garlic and cover the potatoes by about 2 inches with water. Season generously with salt. Bring the water to a boil over high heat, then reduce heat to a simmer and cook until the potatoes are fork tender, about 20 minutes.
While the potatoes are cooking, put 2 tablespoons olive oil into a saute pan, add the bacon and bring to a medium-high heat. Cook the bacon until it is brown and crispy. Remove from the heat and add the onions, celery and vinegar. Season with salt and reserve.
When the potatoes are fork tender, drain them from the water and transfer them to a large mixing bowl. While the potatoes are still hot add the bacon-onion mixture. Stir to incorporate. Add the Mayonnaise and stir to combine. TASTE for seasoning and stir in the mustard. Add more salt, if needed.
Place the egg yolks in the bowl of the food processor and add the vinegar and mustard. Season with salt, to taste. Turn the machine on and VERY slowly start to drizzle in the oil. Drip, drip, drip until the mixture starts to look like mayonnaise, then a slow steady stream of oil can be added.
If the mayonnaise is too thick add a few drops of water or if it is not thick enough, with the machine running, add a little more oil.
Consumption of raw or undercooked eggs, shellfish and meat may increase the risk of foodborne illness.