Heat olive oil in a large saucepan over medium heat. Add the diced chicken and sauté for approximately 15 minutes, ensuring it is fully cooked and no longer pink. Transfer the chicken to a separate dish and keep warm.

In the same pan, combine the chopped onion, sliced mushrooms, minced garlic, and sun-dried tomatoes. Cook over medium heat for 15 to 20 minutes, stirring occasionally, until the onions are softened and the mushrooms develop a rich, golden hue.

Return the cooked chicken to the pan and season with salt and pepper to taste. In a mixing bowl, whisk together the half-and-half, butter, chopped basil, and grated Parmesan cheese. Pour this mixture into the pan and simmer gently, partially covering the pan to allow the flavors to meld.

Prepare the Farfalle pasta according to the package instructions. Drain the pasta thoroughly and incorporate it into the sauce, stirring to ensure the pasta is evenly coated. Serve the dish immediately while warm.