Step 1: Preheat your oven to 375°F (190°C). Lightly grease a 9x13 inch baking dish.
Step 2: In a large bowl, combine the shredded chicken, 1/2 cup sour cream, chili powder, cumin, garlic powder, salt, and pepper. Mix well. Stir in 1 cup of Monterey Jack and 1 cup of Cheddar cheese until combined.
Step 3: To make the creamy sauce, melt butter in a medium saucepan over medium heat. Whisk in the flour and cook for 1-2 minutes until a light roux forms.
Step 4: Gradually whisk in the chicken broth and milk, stirring constantly to prevent lumps. Bring to a simmer, then reduce heat to low.
Step 5: Add the softened cream cheese, onion powder, black pepper, and salt. Whisk until the cream cheese is fully melted and the sauce is smooth and slightly thickened.
Step 6: Dip each tortilla into the warm creamy sauce, just enough to coat lightly. This helps them stay pliable. Place about 1/3 cup of the chicken mixture down the center of each tortilla.
Step 7: Roll up each tortilla tightly and place seam-side down in the prepared baking dish. Repeat with remaining tortillas and filling.
Step 8: Pour the remaining creamy sauce evenly over the rolled enchiladas. Sprinkle the reserved 1 cup of shredded cheese blend on top.
Step 9: Bake for 20-25 minutes, or until the cheese is bubbly and lightly golden, and the enchiladas are heated through.
Step 10: Let the enchiladas rest for 5-10 minutes before serving. Garnish with fresh cilantro or extra sour cream if desired.