Cook the chicken breasts in boiling water or a skillet until fully cooked, then shred with two forks until tender and fibrous.
Puree roasted poblano peppers in a blender along with a bit of enchilada sauce until smooth, then set aside.
Heat olive oil in a skillet over medium heat, sauté chopped onion and minced garlic until fragrant and translucent, about 3-4 minutes.
Stir in smoked paprika into the onion mixture for about 30 seconds until fragrant, then add the shredded chicken and poblano puree, stirring well to combine.
Pour in half of the enchilada sauce and mix everything together, allowing the flavors to meld for a couple of minutes. Remove from heat.
Preheat your oven to 375°F (190°C). Warm the tortillas slightly to make them more pliable, stacking them under a damp towel if needed.
Spread a thin layer of enchilada sauce in the bottom of the baking dish. Spoon a portion of the chicken and poblano mixture onto each tortilla, roll tightly, and place seam-side down in the dish.
Pour the remaining enchilada sauce over the assembled rolled tortillas, ensuring they are well covered. Sprinkle shredded cheese evenly on top.
Bake in the preheated oven for about 20-25 minutes, until the cheese is melted and bubbly, with a slight golden edge on top.
Remove from oven and let rest for a few minutes. Serve hot, garnished with fresh herbs or sliced avocado if desired.
