Heat large pot over medium-high heat. When pot is warm, add neutral oil and continue warming until oil is hot and shimmery.
When oil is hot, add diced onion. Sauté onions 4 minutes or until softened, then add minced garlic. Stir to incorporate and sauté garlic 30 seconds or until just fragrant.
Add chicken broth, green chilies, cumin, paprika, oregano, coriander, cayenne pepper, salt, and black pepper to pot. Stir well to incorporate ingredients. Let mixture come to low boil, then immediately reduce heat to low and simmer 10 minutes.
While mixture simmers, add coconut milk (or coconut cream) and raw cashews to high-speed blender. Blend until mixture is smooth.
After broth mixture has simmered 10 minutes, add cashew cream to pot along with shredded chicken, fresh lime juice, and cilantro. Stir to incorporate and simmer until chicken is warmed through. Taste and adjust seasonings as needed.
Divide soup into preferred portions. Garnish with additional cilantro and diced avocado, and serve immediately.