Char poblano peppers on all sides over a gas flame. If you don't have a gas stove, char them under the broiler. Once all of the pepper is charred, place in a bowl and cover with plastic wrap. Let them sit for 5 minutes. Peel skin off, take stem and seeds out. Season chicken on both sides with 1/2 teaspoon salt, a little bit of black pepper, and ground cumin. Set aside.
While the peppers steam, bring large pot of water to a rolling boil. Season liberally with salt. Cook pasta until just shy of aldente, with fresh pasta this should only be about 3 minutes. Reserve about 1/2 to 3/4 cup of the starchy pasta water. Drain pasta. Set aside.
While pasta cooks, add two peppers, cilantro, 1/2 cup chicken stock and 1/2 cup heavy cream to a blender. Blend until smooth. Slice third pepper into strips.
Once pasta is drained, add poblano cream sauce from the blender to the pot, along with remaining heavy cream, garlic, 1/2 teaspoon salt, and red pepper flakes. Bring to a boil and reduce to a simmer until slightly thickened, about 3 minutes. Add cooked pasta, sliced peppers, remaining 1/4 teaspoon salt, and corn. Toss until pasta has absorbed sauce. Season to taste with salt and pepper. Garnish with chopped cilantro.
As the sauce cooks, heat a medium skillet to a medium heat. Add chicken. Cook 3-4 minutes per side until cooked through. Sliced and serve on top of pasta.