Begin by grinding mushrooms, carrots, and onions using a meat grinder or a food processor. Just pulse the veggies until mostly uniform, stopping often to scrape down sides. Make sure to not over process, leave a little texture. Cook mixture in a few tablespoons of oil. The goal here is to cook out as much water as possible, letting the vegetables caramelize some to add maximum flavor. Once, cooked, set aside to cool.
While your vegetables are cooking, grind your beans and seeds. When the vegetables are cool, add them to the ground beans and seeds. Season with salt and achiote paste. Mix the potato starch and water to make slurry. Add the potato starch slurry to the remainder of the ingredients. Mix well. Divide mix into 6 and form into patties. Let chill in refrigerator for a few hours to firm up.
To cook the patties, heat 1/4 inch cooking oil in a sauté pan. Just when the oil begins to smoke, gently place patties in pan. Being careful to not move the patties, cook for a few minutes until deep golden brown and crispy. Flip and cook the other side. Once cooked, drain on a paper towel and season with a sprinkle of sea salt.
For assembly, toast brioche bun in a little oil or butter. Spread one side of bun with the roasted garlic tahini and the other side of the bun with the guacamole. Layer veggie patty, tomato, pickled red onion, and lettuce and top with bun.
This recipe allows for a little flexibility. Fresh herbs or spices may be added to the patty in place of or in addition to the achiote. And of course the possibilities of burger garnish are endless. Use what you like. Also, mix can be formed into balls and used as a great addition to salads or for wraps.