In a pan, dry toast the walnuts for 3-4 minutes until fragrant and golden brown, then set aside.
Put garlic, onion, and mushrooms in the same pan and sauté for 5-7 minutes until everything is soft, then put in a large bowl.
Add beans into the bowl to the onion, garlic, and mushroom mix and mash well with a wooden spoon.
Using a grinder or food processor, loosely grind the walnuts and oats, then add them to the bowl as well together with all other remaining ingredients except for the buns, the 1 tbsp mustard, and other toppings. Mash and mix until well combined.
Divide into 4 patties of around 1⁄2 inch thickness.
Heat the pan you used earlier over medium heat and add the patties once it is hot enough. Grill on both sides for around 5 minutes until well browned.
Let cool slightly, then assemble burgers by using (toasted) buns, patties, tomato, greens, onion, and mustard.