Whisk flax seeds together with 3 tbsp. water. Set aside and allow to sit for at least 10 minutes.
Heat 1 tbsp. oil in large skillet over medium heat. Add onion and sauté 5 minutes.
Add garlic and cauliflower and sauté another 5 minutes, until cauliflower softens.
Transfer cauliflower mixture to food processor and add remaining burger ingredients, including remaining 1 tbsp. oil. Pulse until well mixed. Shape into 4 patties.
Coat skillet with oil or cooking spray and cook patties about 5 minutes on each side, until browned.
Stir together mayo ingredients and use to top burgers