Place chicken breasts in a large pot, cover with salted water, and bring to a boil. Reduce heat and simmer for 20-25 minutes until internal temperature reaches 74°C. Remove, let cool slightly, then shred with two forks.

Roast poblano peppers directly over a gas flame or under the broiler, turning frequently until charred on all sides, about 8-10 minutes. Place in a bowl, cover with plastic wrap for 10 minutes, then peel, seed, and roughly chop.

Preheat oven to 190°C. Lightly grease a 9x13 inch baking dish.

Heat olive oil in a large skillet over medium heat. Sauté onion until softened, about 5 minutes. Add garlic and cook for 1 minute until fragrant.

Add roasted poblanos, sour cream, chicken broth, cream cheese, cumin, oregano, salt, and pepper to the skillet. Stir over medium-low heat until cream cheese melts and sauce is smooth, about 5 minutes.

Transfer half of the creamy poblano sauce to a blender and blend until smooth. Return to the skillet and stir to combine.

Mix shredded chicken with 120g of Monterey Jack cheese and 120ml of the creamy sauce in a bowl.

Spoon about 3 tablespoons of chicken mixture down the center of each tortilla. Roll up tightly and place seam-side down in the prepared baking dish.

Pour remaining creamy poblano sauce evenly over the enchiladas. Top with remaining Monterey Jack cheese.

Bake uncovered for 20-25 minutes until cheese is melted and edges are bubbling.

Let rest for 5 minutes before serving. Garnish with fresh cilantro and sliced green onions.