Using a box grater or a food processor, grate the yellow onion. Make sure to include the juices, as this adds flavor to the sauce.
In a mixing bowl, combine the grated onion, mayonnaise, sweet pickle relish, yellow mustard, white vinegar, sweet paprika, onion powder, garlic powder, and salt.
Using a whisk or spoon, mix all the ingredients together until well combined and smooth. Taste and adjust seasoning if necessary.
Transfer the sauce to a sealable container and refrigerate for at least 30 minutes. This chilling time allows the flavors to meld beautifully.