Bring a large pot of salted water to a boil and cook the pasta according to the package directions until al dente. Reserve about 1/2 cup of the pasta water, then drain and set aside.
Meanwhile, pat the chicken dry and season with half the salt, pepper, and all the cumin, chili powder, smoked paprika, and oregano. Toss to coat evenly.
In a large skillet over medium-high heat, heat the olive oil. Sear the chicken in a single layer until lightly browned and cooked through, about 5-6 minutes. Remove the chicken and set aside.
In the same skillet, add the bell peppers and jalapeño. Sauté until they soften and start to blister, about 4-5 minutes. Add the garlic and cook for another 30 seconds until fragrant.
Pour in the chicken broth and bring to a gentle simmer. Stir in the cream and half of the cheese, allowing it to melt and form a creamy sauce.
Return the chicken to the skillet, then add the cooked pasta. Toss to coat, adding reserved pasta water a splash at a time to reach your desired sauciness.
Finish with lime juice, remaining cheese, and cilantro if using. Adjust salt and pepper to taste. Serve warm.