Roast the poblano peppers: Preheat your broiler or grill. Place poblano peppers on a baking sheet and broil, turning occasionally, until skins are blackened and blistered all over. Transfer to a bowl, cover tightly with plastic wrap, and let steam for 10-15 minutes. Once cool enough to handle, peel off the skins, remove stems and seeds, and roughly chop the flesh.

Cook the chicken: Season chicken breasts with salt and pepper. Heat 15 ml of olive oil in a skillet over medium-high heat. Sear chicken for 4-5 minutes per side, until cooked through. Let rest, then shred finely with two forks.

Prepare the sauce base: Heat the remaining 15 ml of olive oil in the same skillet over medium heat. Add the chopped onion and sauté until softened, about 5-7 minutes. Add the minced garlic and cook for 1 minute more until fragrant.

Build the sauce: Stir in the minced chipotle peppers and adobo sauce, cumin, and smoked paprika. Cook for 1 minute, stirring constantly. Pour in the chicken broth and bring to a simmer, scraping up any browned bits from the bottom of the pan. Let simmer for 5 minutes.

Blend the sauce: Carefully transfer the skillet mixture to a blender. Add the roasted poblano peppers and heavy cream. Blend until very smooth. Return the sauce to the skillet and season with salt and pepper to taste. Keep warm over low heat.

Assemble the enchiladas: Preheat oven to 191 °C (190 °C). Lightly warm the corn tortillas in a dry skillet or microwave to make them pliable. Spread about 120 ml of the poblano sauce in the bottom of a 9x13 inch baking dish.

Fill and roll: Dip each tortilla briefly into the warm sauce (or use a brush to coat). Place about 60 ml of shredded chicken and 30 ml of shredded cheese down the center of each tortilla. Roll up tightly and place seam-side down in the prepared baking dish.

Bake: Pour the remaining poblano sauce evenly over the rolled enchiladas. Sprinkle the remaining shredded cheese over the top. Bake for 20-25 minutes, or until the sauce is bubbly and the cheese is melted and lightly golden.

Rest and serve: Let the enchiladas rest for 5-10 minutes before serving. Garnish with fresh cilantro and serve immediately with lime wedges on the side.