Preheat your oven to 400°F (200°C).

Begin by roasting the poblano peppers. Place them directly over an open flame or on a baking sheet under the broiler, turning occasionally, until the skin is charred and blistered (about 10-15 minutes). Once roasted, cover with plastic wrap to steam for about 10 minutes.

Season the chicken breasts with smoked paprika, dried oregano, salt, and pepper.

In a large oven-safe skillet, heat olive oil over medium-high heat. Add the seasoned chicken breasts and sear for about 5-6 minutes on each side until golden brown. Remove the chicken from the skillet and set aside.

Once the poblano peppers have cooled, peel off the charred skin, remove the seeds, and chop them into small pieces.

In the same skillet, add minced garlic and sauté for about 30 seconds until fragrant. Add the chopped poblano peppers and heavy cream, stirring to combine and bringing to a simmer.

Add the grated Parmesan cheese to the skillet, stirring until melted and the sauce is smooth. Season with additional salt and pepper as needed.

Return the seared chicken breasts to the skillet, spooning the poblano Parmesan sauce over the top.

Transfer the skillet to the preheated oven and bake for 20-25 minutes, or until the chicken is cooked through (165°F/74°C).

Once done, remove from the oven and let it rest for a few minutes. Garnish with fresh cilantro sprigs before serving.