In a large nonstick skillet over medium-high heat, add olive oil and diced chicken breast. Heat until chicken is cooked through.
Add spices and water. Continue to cook until chicken is coated in herbs and water has reduced. Remove from heat and set aside.
In a medium saucepan over medium heat, combine jar of salsa verde, 2 small cans of diced green chiles, lime juice, sugar, and cream. Stir continuously until it's bubbly slightly, and sugar is dissolved well.
Remove from heat and pour into blender. Blend until smooth (can also use an immersion blender). Set aside.
Preheat oven to 325°F. Spray a 9x13 pan with cooking spray.
In a large bowl, combine cooked chicken, 1 cup of cheese, 1 can of diced green chiles, black beans, and cooked rice. Mix well.
Place a flour tortilla in one hand, and scoop 1-2 heaping scoops of the enchilada filling into the tortilla. Spread it evenly, vertically, along the tortilla. Roll it up well and place in the prepared 9x13" pan.
Continue filling and rolling until pan is full. Pour sauce over enchiladas, then top with remaining 2 cups of cheese.
Bake in preheated oven 15-20 minutes, until cheese is bubbling and/or golden brown.
Remove from oven and top with fresh cilantro and/or more lime juice. Enjoy!