Heat the oven to 425°F and arrange two racks to divide the oven into thirds.
Arrange the bacon pieces in a single layer on 2 rimmed baking sheets. Bake for 10 minutes. Rotate the pans between the racks and continue baking until the bacon is crisped and brown, about 5 to 10 minutes more.
Transfer the bacon pieces to a large paper-towel-lined plate, placing additional paper towels between each layer of bacon. Carefully pour the bacon fat from the baking sheets into a heatproof measuring cup—you need 2/3 cup. (If you don’t have enough bacon fat, add vegetable oil as needed.) Discard any excess bacon fat. Let the measured bacon fat cool for 15 minutes.
Place the egg yolks, vinegar, and mustard in a medium bowl and whisk until combined. While whisking constantly, very slowly add the bacon fat or bacon fat–oil mixture in a thin stream until it’s completely incorporated and the mixture is thickened and creamy. Add the salt and pepper and whisk to combine; use immediately or refrigerate for up to 4 days.