Optional: Barbecue sauce, toasted hamburger buns, Sriracha mayo, lettuce, red onion and tomato
Preheat oven to 325°. Spread beans evenly on a parchment-lined rimmed baking pan. Bake until beans start to split open, 6-8 minutes.
Meanwhile, in a large dry nonstick skillet over medium heat, cook and stir walnuts, cumin, fennel and smoked paprika until fragrant, 2-3 minutes. Remove from pan and cool. In the same skillet, heat oil from sun-dried tomatoes over medium heat. Add carrot, shallot and sun-dried tomatoes; cook and stir until tender, about 5 minutes. Add garlic; cook 1 minute longer. Remove from the heat; cool slightly.
Transfer carrot mixture to a food processor. Add beans, walnut mixture, oats, chia seeds, soy sauce and garlic salt. Pulse until combined. Shape into four 4-in. patties.
In the same skillet over medium heat, cook patties in olive oil until browned, 3-4 minutes on each side. If desired, baste with barbecue sauce and serve on buns with toppings of your choice.