Fill a saucepan 3/4 full of water and pour in salt. Bring to a boil.
Add chicken and garlic cloves to the water. Reduce heat to medium low, keeping water at a simmer. Cook chicken 15 minutes.
Preheat oven to 375 degrees. Lightly grease a 9x13 pan.
Remove cooked chicken from water and transfer to a mixing bowl. Shred the chicken with a fork. Season with cumin and chili powder. Pour in 1 cup of the mole verde and 1/2 cup sour cream, 1 cup shredded mozzarella, and the cilantro. Stir until combined. Gently fold in diced avocado.
Roll enchiladas by placing a scoop of the chicken mixture into the center of a corn tortilla. Fold ends in and roll. Place in prepared 9x13 pan. Repeat with remaining tortillas. Pour mole verde sauce over all enchiladas to completely smotoher them with sauce. Sprinkle remaining shredded mozzarella cheese over the tops of the enchiladas.
Bake in the preheated oven until cheese is starting to brown, about 30 minutes.