Place walnuts and dried shiitake mushrooms in the bowl of a food processor and process until finely ground, 30-45 seconds. Transfer to a bowl and set aside.
To make the Vegan Chili: Heat olive oil in a heavy bottom pan (like a Dutch oven) over medium-high heat. Add in onion, celery, and jalapenos. Cook, stirring frequently, until onions begin to brown, 7-9 minutes.
Reduce heat to medium and stir in cumin, chili powder, tomato paste, and garlic. Cook, stirring constantly, until fragrant, for about 1 minute.
Add in diced tomatoes, black beans, Cannellini beans, vegetable stock, soy sauce, bulgur, and the processed walnut-shiitake mushroom mixture.
Put the lid on, bring the mixture to a boil, and then let it simmer until it thickens to your liking, 25-30 minutes. The longer it simmer the thicker it will become.
Stir in the cilantro right before serving.
Ladle into bowls and top it off with the garnishes.