If you go to http://www.dominos.uk.com/pdf/FoodGuide_Starters.pdf
, you will see that the ingredients for the Domino's Garlic & Herb Dip are as follows:Vegetable Oil, Pasteurized Egg Yolk, Water, Vinegar, Garlic, Sugar, Parsley, Lactic Acid, Lemon Juice, Salt, Milk Protein, Mustard, Potassium Sorbate, Sodium Benzoate, Guar Gum, Xanthum Gum.
Vegetable oil in the above list is technically soybean oil. Soybean oil, pasteurized egg yolk, water, vinegar, sugar, lemon juice and salt, collectively, are really a form of mayonnaise. Potassium sorbate and sodium benzoate are preservatives. Unless you are planning on making a large quantity of the dip to use over a relatively long period of time, you shouldn't need these preservatives although it is possible that they contribute to the overall flavor profile for the dip. Guar gum and xanthum gum are thickeners (emulsifiers). Both can be purchased for home use. In fact, these are gums that are frequently used by people with celiac's disorder for making gluten-free pizza doughs.
You might try a commercial mayonnaise or make your own and add some garlic (fresh or a powder), parsley and mustard. You might get a better consistency and stability by using the guar and xanthum gums. To get the right amount of garlic, parsley and mustard, you might do a side-by-side analysis using a known quantity of mayonnaise (by weight or volume) and a sample of the Domino's Garlic & Herb Dip, and individually add the garlic, parsley and mustard to the mayonnaise until the flavors match as best as possible the flavors of the Domino's dip. This is not a technically proper way of creating the match but it may be one of the few options you have. To be able to make a future batch, you will want to note the amounts of garlic, parsley and mustard (by weight or volume) that you add to your mayonnaise sample.