Mix all the sauce ingredients in a bowl and set aside.
To make the patties:
In a frying pan on medium heat, add a little coconut oil. When hot, add the chopped onions, garlic and carrot. Cook, stirring occasionally until the onion is translucent and soft.
In a large bowl add the beans, mash them until smooth with a masher or vertical blender, add the oats and blend a few more times. You can also use a food processor. Then add all the rest of ingredients and the cooked onion mixture. Mix everything until well incorporated. Let sit for about 10 minutes, so all the flavors are mixed and the liquid is absorbed.
Form 8 patties.
Heat a large skillet on medium heat. Add a little coconut oil and cook the patties in batches, for about 4 minutes on each side.
To make the Big Mac, lightly roast the bun slices.
On the first bottom bun, add ½ Tbsp sauce, 1 Tbsp shredded lettuce, ½ tsp chopped onion, a slice of cheddar, 1 vegan patty and 2 slices of pickled cucumber.
Top with the next slice of the bun and repeat for all the ingredients, except the cheese. Cover with the bun top and serve with extra sauce or ketchup.