Cook the beans. Add the soaked beans into a medium pot, cover with water by several inches, and bring to a boil over high heat. Reduce the heat to medium-low, season with salt, and simmer, uncovered, until the beans are fully tender, 45-90 minutes (depending on the size/freshness of your beans). Top with water as necessary to keep the beans submerged at all times. Sample a bean at the 40-minute mark to see how tender the beans are. You're looking for a just tender bean with a tiny bit of bite. Once cooked, drain the beans.
Preheat the oven. Arrange a rack in the middle of the oven. Heat the oven to 400ºF/204ºC.
Sauté the aromatics and mushrooms. Heat the olive oil in a medium skillet over medium-high heat. Add the onion and garlic and sauté until translucent, 5-7 minutes. Add the mushrooms, season with salt, and sauté until the mushrooms have softened and reduced in size, 5-7 minutes.
Process the walnuts. Add the walnuts into a food processor fitted with the S blade and pulse into a coarse meal. Make sure not to over-process the walnuts.
Pulse. Add the cooked beans, sautéed mushrooms, chickpea breadcrumbs, flax egg, tomato paste, ground cumin, smoked paprika, and salt into the food processor with the chopped walnuts and pulse to loosely combine, pausing to scrape down the sides as necessary. Be careful not to purée. If the mixture is too wet, add more chickpea breadcrumbs. If it's too dry, pulse a little more.
Season. Taste and adjust the flavor as needed, adding more salt for saltiness, garlic for pungency, cumin for earthiness, and smoked paprika for smokiness.
Form patties. Scoop out about ¼ cup of the burger mixture and pack it firmly between your hands to form ½-in/1.3-cm thick patties. Repeat until all the veggie burger mixture is used up. Brush the patties with a little bit of olive oil before baking, so they crisp up nicely on the outside while staying moist on the inside (as opposed to drying out).
Bake. Place the veggie burgers on a parchment paper-lined baking sheet or a well-seasoned cast iron griddle and bake until golden brown, about 20 minutes. Let cool slightly to firm up, 5-10 minutes.
Serve the veggie burgers in a bun or atop mixed greens with desired toppings. Some of my favorite toppings include lettuce, caramelized onions, sautéed mushrooms, avocado, sprouts, and mustard.
Store. Leftover veggie burgers keep well covered in the refrigerator for 4-5 days. For longer term storage, freeze uncooked pre-shaped burger patties in an airtight container, separating each row with a piece of parchment paper (so the veggie burgers don't stick to each other as they freeze) for up to 3 months. (You can freeze cooked burgers as well, but they are never quite as good).
Reheat in a 400ºF/204ºC oven until heated through and crispy again, for about 5 minutes. If reheating frozen (uncooked) veggie burgers, transfer the veggie burgers into the refrigerator 24 hours before baking to thaw. Once thawed, follow the instructions for baking above.