In a large pot or Dutch oven set over medium-high heat, add the butter or olive oil. Once melted, add the chopped yellow onion and chicken. Cook for 5-7 minutes, stirring occasionally, until the chicken is lightly browned and the onion is softened.
Stir in the chopped garlic, poblano peppers, ground cumin, smoked paprika, chili powder, and a pinch each of salt and pepper. Cook for another 2-3 minutes until fragrant. Pour in the 4 cups of chicken broth. Partially cover and simmer over medium-low heat for 10-15 minutes until the chicken is cooked through.
Carefully remove the cooked chicken from the pot and shred it using two forks. Set aside. To the pot, add the elbow macaroni and 2 cups of water. Bring to a boil over medium-high heat, then reduce heat to medium and simmer for 8-10 minutes, or until the pasta is al dente, stirring often to prevent sticking.
Reduce the heat to low. Stir in the softened cream cheese, shredded chicken, rinsed and drained cannellini beans, salsa verde, diced green chiles, and 1 cup of the shredded cheese. Cook for another few minutes, stirring constantly, until the sauce is creamy and the cheese is melted.
Preheat your oven to 425°F. Remove the pot from the heat and top the chili mac with the remaining 1 cup of shredded cheese. Bake for 5-10 minutes, or until the cheese is melted and bubbly.
Divide the creamy white chicken chili mac among bowls and garnish with chopped green onions and fresh cilantro before serving. Enjoy!