In a small bowl, mix together the ground flax and water to make flax eggs. Set aside about 10 minutes to thicken up and become gel-like.
In a large bowl, mash the drained beans with a fork or potato masher. Add the rice, walnuts, oats, arrowroot powder, prepared flax eggs, tomato paste, worcestershire sauce, tamari and liquid smoke. Combine really well and set aside.
In a large pan, heat oil over medium heat. Add onion and sauté for 3-4 minutes, until translucent. Add garlic and sauté for 30-60 seconds until fragrant.
Add the mushrooms and turn the heat up to medium-high. Sauté until they release their liquid and brown. Cook liquid completely off or there will be too much moisture. About 6-7 minutes. Now turn the heat back to medium and add the paprika, cumin and oregano. Sauté for 30-60 seconds. Remove from heat.
Transfer the cooked mixture into the large bowl of previously mixed ingredients. Combine well, using hands if necessary. Add cracked pepper and taste and add more seasoning if needed. Place mixture uncovered in the freezer for 25 minutes or the fridge for 45 minutes or more. This helps firm it up and meld the flavors a bit.
Form the mixture into individual patties, keeping the size of the burger buns in mind. Create a ball with the mixture and place on a large piece of parchment paper. Now flatten evenly with your hands to create a ½" disc. Smooth out sides and any cracks with your hands. Repeat until the mixture is gone. * I used ½ cup of mixture to form ½" thick patties to fit a 3.5" burger bun.
Line a large baking sheet with parchment paper. * Optional: lightly spray with cooking oil for a crisper surface. Place in the oven for 16-18 minutes until lightly browned. Flip halfway through. When finished, remove from oven and let them cool for 5 minutes before handling (to let them firm up a bit). At this point, you can eat them, refrigerate or freeze them.
Place 1-2 tablespoons of cooking oil in a large pan over medium heat. Make sure the oil is hot and shimmering before adding the uncooked patties (*The patties should sizzle when you place them on the pan). Don't overcrowd the pan or the patties will steam. Sear each side for about 3 minutes until crisp and brown. If you flip the patty to early, it will stick to the pan. It should lift up easier when the side is seared. Be gentle while flipping. Place them on a paper towel-lined plate and let them sit for 5 minutes to firm up. At this point, you can eat them, refrigerate or freeze them.
Spead vegan mayo on the burger buns. Dress burger with vegan cheese, lettuce, sliced tomato, red onion, pickles, mustard, and ketchup. Enjoy!
