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