Heat olive oil in a large skillet over medium-high heat.
In a medium bowl, combine chicken pieces, ground cumin, garlic powder, chili powder, salt, and black pepper. Toss to coat evenly.
Add the seasoned chicken to the hot skillet and cook for 5-7 minutes, stirring occasionally, until the chicken is browned and cooked through.
Reduce heat to medium and add diced green chilies and chicken broth to the skillet. Stir to combine and bring to a simmer.
Cook for 5 minutes, allowing the sauce to reduce slightly.
Remove the skillet from heat and stir in sour cream until the sauce is creamy and well combined.
Sprinkle shredded Monterey Jack and cheddar cheeses evenly over the chicken and sauce.
Return the skillet to low heat and cover with a lid. Cook for 3-5 minutes until the cheese is melted and bubbly.
Remove from heat and garnish with sliced green onions.
Serve immediately with rice, tortillas, or your favorite side.