Toast walnuts and sunflower seeds in a skillet until golden and fragrant. Remove from skillet and sauté onion with olive oil until translucent.
In a food processor, blend toasted walnuts and seeds with chili powder, cumin, smoked paprika, salt, and pepper until a fine meal is achieved.
In a large bowl, mash black beans. Add cooked rice, spiced walnut mixture, sautéed onion, panko breadcrumbs, and BBQ sauce. Mix until a moldable dough forms.
Divide the mixture into 4 equal parts and shape into patties.
Heat a skillet over medium heat, lightly oil it, and cook patties for about 4 minutes on each side or until well browned and heated through.
Serve the veggie burgers on buns with toppings and condiments, such as vegan mayonnaise.