Bring a large pot of water to a boil, add 1/2 tablespoon salt, and cook the penne according to package directions until al dente; drain and toss with 1 1/2 tablespoons unsalted butter to keep the noodles from sticking.
Season the chicken with salt, pepper, and your preferred seasoning (for example, Garlic Mrs. Dash). Grill or sauté the chicken over medium-high heat until fully cooked, then let rest briefly and slice against the grain.
Heat a large or deep skillet over medium-high heat and add 1 tablespoon butter plus 1 tablespoon olive oil.
Add the sliced bell pepper, sliced mushrooms, and diced onion to the skillet and sauté until softened, about 8 minutes; season the vegetables with 1/8 teaspoon freshly ground black pepper and 1/2 teaspoon salt.
Stir the drained pasta, chopped sun-dried tomatoes, and sliced cooked chicken into the skillet with the vegetables and mix to combine.
Pour in 2 cups heavy whipping cream, add 3/4 cup shredded Parmesan cheese and 1/4 cup sweet chili sauce if using, then stir and return the pan to medium heat.
Cook, stirring frequently, until the sauce is heated through, creamy and the cheese is melted, about 3–5 minutes; adjust seasoning if needed and serve.
