Preheat an oven to 350ºF. Line a baking sheet with parchment paper.
Toast the beans and walnuts. In a mixing bowl, toss the walnuts and black beans with 1 tablespoon of olive oil and a sprinkling of salt and pepper. Spread them in an even layer on the prepared baking sheet and bake for 20 minutes. Remove and let cool.
Pulse to mince. While the beans and walnuts cool, pulse the oats in a food processor until finely minced. Add the cooled black beans and walnuts and pulse until no large pieces remain.
Make the burger mixture. In the same bowl you used to toss the walnuts and beans, whisk together the remaining ingredients including the spices, salt, and pepper. Fold the black bean mixture into the wet ingredients until well-mixed.
Shape the patties. Divide the mixture into 4 equal portions and shape into tight patties. Transfer to a plate and refrigerate for 20 minutes. (Shaping the patties into very compact pucks is what prevents them from falling apart on the grill.)
Preheat an outdoor grill or grill pan over medium-high heat. If grilling outdoors, clean and oil the grill grates really well. Grill the burgers for 4-5 minutes per side, until warmed through with grill marks.
Assemble. Place the burgers on toasted buns with your desired sauces and toppings, then serve.