In a large pot over medium heat, warm the oil or butter. Add the onion, carrots, and celery, and ½ teaspoon salt and cook for 5 minutes or until softened, stirring occasionally.
Add the mushrooms, garlic, thyme, and remaining ½ teaspoon salt and cook for 1-2 more minutes, stirring often. Stir in water, potatoes, chicken, and soy sauce. Cover and bring to a boil over high heat, then give it a stir (submerging everything in the liquid) and reduce the heat to low or medium-low to simmer for 10-15 minutes or until the potatoes and chicken are cooked through (may vary depending on size of chicken). Remove the chicken and shred it up.
Meanwhile, drain the cashews and add them to a high-speed blender along with ½ cup of tap water + ½ cup broth/liquid from the soup (it’s okay if chunks get in there). Blend until totally smooth (about 1 minute, scraping down sides as needed), then stir back into the pot along with the shredded chicken and peas.
Serve topped with black pepper and crackers, if using.