In a mortar and pestle, mash the onion to create a paste, or use a large heavy knife to mince and mash the onion into a paste.
Transfer the onion paste to a small bowl and whisk in the mayonnaise, chili sauce, horseradish, hot sauce, Worcestershire sauce, and sweet paprika.
Season with fine sea salt, if desired.
DO AHEAD: The dressing can be prepared ahead and refrigerated, in an airtight container, up to 2 weeks.
