Roast your poblano peppers over an open flame or under the broiler until the skin is charred and blistered. Place them in a sealed bowl or plastic bag to steam for about 10 minutes, then peel off the skin, remove the seeds, and chop finely. For extra creaminess, puree in a blender if desired.
Bring a large pot of salted water to a boil. Add the penne and cook according to package instructions until al dente. Drain and set aside, reserving a bit of pasta water.
Heat 2 tablespoons of olive oil in a large skillet over medium-high heat. Add the diced chicken breast, season with salt, pepper, cumin, and paprika, and cook until golden brown and cooked through, about 6-8 minutes. Remove chicken and set aside.
In the same skillet, add chopped onion and minced garlic. Sauté until soft and fragrant, about 3-4 minutes. Stir in the roasted poblanos, then pour in chicken broth and heavy cream. Let simmer gently, thickening slightly, about 5 minutes.
Return the cooked chicken to the skillet and stir in shredded cheddar cheese. Continue stirring until cheese melts and sauce is creamy and smooth. Adjust salt and pepper as needed.
Add the drained penne pasta to the skillet, tossing everything together so each piece is coated in the creamy poblano chicken sauce. If sauce is too thick, add reserved pasta water to loosen.
Plate the Creamy Poblano Chicken Penne and sprinkle with fresh cilantro leaves. Serve immediately and enjoy.