Chop the mushroom caps into quarters and place them in the bowl of a food processor. Close the lid and pulse the mushrooms until they are all finely minced. Set aside.
Heat the oil in a large, heavy pot over medium heat. Add the onion to the pot and saute until slightly soft, about 3 minutes. Add the carrots and celery. Saute the vegetables until all are slightly softened, about 4 minutes. Add the minced mushrooms to the pot and stir. Keep stirring and cooking the mushrooms until they glisten and soften up slightly, about 2 minutes.
Add the garlic, miso, and smoked paprika to the pot and stir until garlic is fragrant, about 30 seconds. Add the Buffalo-style sauce, tomatoes, chickpeas, and vegetable stock to the pot. Stir to combine and then bring the chili to a boil.
Simmer the chili, uncovered, for about 15 minutes, stirring occasionally. Everything in the Buffalo chickpea chili is already cooked, but you want to marry the flavours before serving. The carrots should be soft when you’re done. Season the chili to taste with salt, pepper, and more Buffalo sauce if desired. Serve the chili hot with cashew sour cream, toast etc.