To make aioli, whisk together Dijon mustard, egg yolk, and lemon juice together in a bowl. Slowly drizzle in olive oil, starting with just a few drops, while whisking. Keep adding the olive oil until the mixture emulsifies and thickens. You should be able to turn the bowl upside down and nothing drips out once it is ready! Reserve for assembling burgers.
To make the za’atar, stir all ingredients together.
Combine ground beef, onion, and za’atar seasoning together until mixed. Don’t over mix. Form into four to six large patties about 3/4-inch thick.
Put the burgers on a lightly oiled pre-heated grill over medium heat or grill pan and grill for about 5 minutes per side until cooked to desired doneness and has an internal temperature of 160 degrees F.
To assemble, put burgers on the bottom side of a bun and top with aioli. Top with lettuce, tomatoes and red onion or desired toppings. Serve and enjoy!