Add enough water to a 4-6 quart pot for cooking the pasta, per package directions. Set over heat to bring water to a boil.
In the meantime while water is coming to a boil, to a deep skillet over medium heat, saute onions and garlic in hot olive oil until onions are just turning translucent.
For the marinated artichoke hearts, remove any tough portions and cut artichokes into chunky pieces. Add artichokes, sun-dried tomatoes, roasted peppers, kalamata olives, capers, and red pepper flakes to the onions and garlic. Stir to combine. Add the diced chicken and stir to combine. Heat gently over medium low or low heat until hot, stirring often.
While vegetables and chicken are heating, cook pasta to the al dente stage. Reserve approximately 1/2-3/4 cups pasta cooking liquid. Set aside. Drain pasta in a colander. Return pasta to the pot in which it was cooked. Add the torn basil leaves to the pasta. Toss gently. Gently stir in the Parmesan until well combined.
To the reserved artichoke marinade, add enough pasta water to make 1 cup. Pour over pasta and stir gently. Add the hot chicken and vegetable mixture to the hot pasta mixture. Stir gently until well combined. Add a little more pasta water if needed for moisture. Taste and add salt as needed.
Serve immediately, topped with additional grated Parmesan.