Make the mayonnaise: Put the egg yolks in a food processor and add the vinegar, mustard and 1/4 teaspoon salt. Turn on the machine and very slowly start to drizzle in the oil (drip until the mixture starts to look like mayonnaise, then you can start adding it in a slow, steady stream). If the mayonnaise is too thick, add a few drops of water; if it is not thick enough, add a little more oil with the motor running.
Make the salad: Put the potatoes and garlic in a large pot. Add enough water to cover the potatoes by 2 inches and season generously with salt. Bring the water to a boil over high heat, then reduce the heat to medium and simmer until fork-tender, about 10 minutes.
Meanwhile, cook the bacon in the olive oil in a large skillet over medium-high heat, stirring occasionally, until browned and crisp, about 10 minutes. Remove from the heat and stir in the onion, celery and vinegar. Season with salt.
Drain the potatoes and transfer them to a large bowl (discard the garlic). Add the bacon-onion mixture to the hot potatoes and stir to incorporate. Gently stir in 1 1/2 cups mayonnaise and the mustard and season with salt. Refrigerate until cold.
Photograph by Yunhee Kim
Recipe courtesy of Anne Burrell for Food Network Magazine