Whisk all ingredients, except for the vegetable oil or olive oil, together in a bowl.
Pour the vegetable oil into the mixture slowly, whisking continuously.
Pour the mixture into a food processor.
Pulse for 45 to 60 seconds, until all ingredients are well-incorporated and the Creole Mustard Vinaigrette is thick and creamy.
Serve immediately, or cover and refrigerate for up to 2 days.
Notes
I've also used apple cider vinegar with great results. It turned out a tad tart, so I added more honey and a sprinkling of brown sugar to balance it out.