In a medium saucepan, heat the olive oil over medium heat. Whisk in the flour and cook for one minute until it's lightly golden. Add the chili powder, smoked paprika, cumin, garlic powder, onion powder, and oregano. Stir constantly for about 30 seconds until fragrant. Gradually pour in the chicken broth while whisking continuously to prevent lumps. Stir in the tomato sauce. Bring the mixture to a simmer, then reduce the heat and let it gently bubble for 5-7 minutes, until it has thickened slightly. Season with salt and pepper to taste. Set aside.

Heat the vegetable oil in a small skillet over medium-high heat. Using tongs, carefully place one tortilla in the hot oil for about 10-15 seconds per side. It should be soft and pliable, not crispy. Transfer the fried tortilla to a plate lined with paper towels to drain excess oil. Repeat with the remaining tortillas.

In a large bowl, combine the shredded chicken, softened cream cheese, 1 cup of Monterey Jack cheese, diced onion, and drained green chiles. Mix until everything is well combined.

Preheat your oven to 375°F (190°C). Pour about 1/2 cup of the enchilada sauce into the bottom of a 9x13-inch baking dish and spread it around to coat. Take one of the pliable tortillas and dip it into the remaining enchilada sauce, coating both sides. Place a generous scoop (about 1/4 cup) of the chicken mixture down the center of the tortilla. Roll it up tightly and place it seam-side down in the prepared baking dish. Repeat with the remaining tortillas and filling.

Pour the rest of the enchilada sauce evenly over the rolled tortillas in the dish. Sprinkle the 3 cups of shredded cheese blend on top. Bake for 20-25 minutes, or until the sauce is bubbly and the cheese is completely melted and slightly golden. Let the enchiladas rest for 5-10 minutes before serving. Garnish with your favorite toppings and enjoy!