Line a slow cooker with a slow cooker bag.
Combine onion, garlic, and oil in a small bowl and microwave for 3 minutes, stirring once.
To slow cooker add, onion and garlic mixture, enchilada sauce, green chilis, salt, pepper, paprika, ancho chili powder, and cumin.
Whisk together water and chicken base. Add to slow cooker. Add chicken to slow cooker.
Cook on low for 6 hours.
Remove chicken from slow cooker, allow to cool for a few minutes and shred or chop.
While chicken cools, add corn to slow cooker.
Whisk together Neufchatel cheese and Greek yogurt. Temper by whisking in some of the hot broth until smooth. Add to slow cooker.
Add chicken back to slow cooker.
Ladle into bowls and garnish with cheese, cilantro and a squeeze of fresh lime.