Char the poblano peppers over a gas flame or under the broiler until blackened and blistered. Place in a covered bowl for 5 minutes to steam, then peel and chop.

Season chicken breasts with coarse kosher salt, black pepper, and ground cumin. Heat olive oil in a skillet and cook chicken for 3-4 minutes on each side until cooked through, then slice and set aside.

Bring a pot of salted water to a boil. Cook fresh tagliatelle until al dente, about 3 minutes. Reserve a cup of pasta water, drain, and set aside.

In a blender, combine roasted poblano peppers, cilantro, chicken stock, and half of the heavy cream. Blend until smooth.

In the same pot used for pasta, pour in the blended poblano sauce, remaining heavy cream, minced garlic, and crushed red pepper flakes. Bring to a simmer and thicken slightly, about 3 minutes.

Add cooked pasta, sliced peppers, and corn to the sauce. Use reserved pasta water if needed for desired consistency. Adjust seasoning and toss to coat.

Plate the creamy pasta mixture and top with sliced grilled chicken. Garnish with fresh cilantro.