In a small saucepan over medium heat, melt the butter. Whisk in the flour and cook for about 1 minute. Gradually whisk in the chicken broth, then add tomato paste, chili powder, smoked paprika, and a pinch of sugar. Simmer for 4–5 minutes until slightly thickened. Season with salt.

Heat vegetable oil in a skillet over medium heat. Sauté the chopped onion for 3–4 minutes until softened. Add minced garlic, cumin, and chili powder and cook 30 seconds. Stir in shredded rotisserie chicken and diced green chiles. Remove from heat and season with salt and pepper.

Preheat oven to 375°F (190°C). Pour 1/2 cup of sauce into the bottom of a 9x13-inch baking dish. Warm tortillas until pliable. Place about 1/3 cup of filling and a sprinkle of cheese in each tortilla, roll, and place seam-side down in the dish.

Pour remaining sauce over the enchiladas and top with remaining shredded cheese. Bake 15–18 minutes until cheese is melted and bubbly. Broil 1–2 minutes for a browned top if desired. Garnish with cilantro and lime wedges before serving.