Blend roasted red peppers, cherry tomatoes, walnuts, garlic, parsley, olive oil, vinegar, smoked paprika, and cayenne in a food processor. The sauce should be smooth and creamy with a vibrant red hue.
Season chicken pieces with Italian seasoning, smoked paprika, and chili flakes. Heat olive oil in a large pot and sear chicken until golden brown and cooked through. Remove and set aside.
In the same pot, add water and bring it to a boil. Add pasta and cook until just tender. Do not drain the water; it helps the sauce cling to the pasta.
Pour the roasted red pepper sauce into the pot with pasta, then stir in Manchego cheese and fresh basil. Toss until everything is creamy, smooth, and well-coated.
Return the cooked chicken to the pot and mix gently to combine. Heat through for 2–3 minutes so the flavors meld together.