Start by prepping the ingredients. Mince the garlic clove finely and cube the cucumber; also, dice the onion finely.
In a large bowl, whisk together mayonnaise, sour cream, egg yolk, ketchup, white vinegar, and sugar until everything is well blended.
Incorporate the minced garlic, diced cucumber, and onion into the mayonnaise mixture. Stir until everything is well mixed together. Now add mustard, vegetable oil, salt, liquid smoke, paprika, and lemon juice to the bowl.
Blend all ingredients together until you achieve a smooth mixture with no lumps left. Transfer the slaw to a dish before serving it either chilled or at room temperature. Enjoy this delightful accompaniment with chips, crackers, sandwiches, and burgers.