In a skillet over medium high heat brown the chicken in batches. You are looking for browning on each side. Adjust heat so that the flavor developing in the bottom of the pan (fond) doesn’t burn. When chicken is brown transfer to a bowl
Add onions to the skillet you browned the chicken in. Add a pinch of salt. If you didn’t adjust the heat while browning chicken you may need to do so now, so the crispy flavor bits (fond) don’t burn. Let the onion sit for a minute and then add a dash of wine to deglaze the bottom of the pan. You made need to continue to add dashes of wine, up to half a cup, throughout the process. Let the onions sweat without burning or caramelizing. Once the onions are cooked through add the garlic. Stir the garlic in and let cook for 1-2 minutes, making sure the bottom of the pan doesn’t burn.
Pour in the remainder of the wine and let reduce to about a 1/4 cup.
Once the wine is finished reducing add in the green pepper. Give it a stir and let it nearly cook through. Once the green pepper is nearly cooked through add in the roasted red pepper and hot cherry peppers. Stir in and let sit for a few minutes to let flavor develop.
Add in the can of whole tomatoes. You can break up the tomatoes with your hands or with a potato masher. Pour in any excess puree. Give it a stir. If you haven’t turn your heat down to low or med low and let the sauce simmer.
While the sauce simmers start your water boiling for the pasta. Salt the water generously so that it tastes like the sea. Once the water is at a boil, dump in the rigatoni and cook until al dente. Just before the pasta is cooked add a half cup of pasta water to your sauce and stir in. Remove pasta from heat and transfer to a colander.
As the pasta drains and dries out a bit, individually add the butter, cream, and parmesan to the sauce allowing each new ingredient to incorporate before adding the next. Taste for seasoning. Add salt and pepper as needed.
Return your cooked rigatoni to the pot. Add the cooked chicken to the sauce. Give a stir. Then pour the sauce into the pot with the rigatoni.
Give the rigatoni a stir. Add in 2 tbs of the fresh basil. Then gently stir the sauce until the rigatoni is well coated. Serve with parm and a little extra fresh basil.