Bring a large pot of salted water to a boil and cook the penne according to package instructions using 1/2 tbsp salt; drain and toss with 1 1/2 tbsp unsalted butter to prevent sticking. Set aside.
Season the chicken on both sides with salt, pepper and your preferred seasoning.
Grill or sauté the chicken over medium-high heat until fully cooked through; transfer to a cutting board, let rest briefly, then slice against the grain.
Heat a large deep skillet over medium-high heat and add 1 tbsp butter and 1 tbsp olive oil.
Add the sliced bell pepper, sliced mushrooms and diced onion and sauté until soft, about 8 minutes. Season the vegetables with 1/8 tsp freshly ground black pepper and 1/2 tsp salt.
Return the cooked pasta and sliced chicken to the skillet with the vegetables, then stir in the chopped sun-dried tomatoes.
Pour in 2 cups heavy whipping cream, add 1/2 cup sweet chili sauce if using, and sprinkle in 3/4 cup shredded Parmesan. Stir to combine and heat gently, stirring occasionally, until the sauce is creamy and the cheese is melted.
Taste and adjust seasoning if needed, then serve warm.