All ingredients ready? Let's begin!
Place the chicken breasts in a baking dish or bowl. Add 1-1/2 tablespoon of kosher salt. Add enough filtered water to cover the chicken.
Cover the dish and place it in the refrigerator for at least 30 minutes and up to 4 hours.
Remove the chicken from the fridge. Rinse it well under cold running water and pat dry with paper towels. Cut the chicken breasts into 1-inch cubes.
In a large skillet or Dutch oven over medium-high heat, warm 1-1/2 tablespoons of the olive oil. Add the chicken, season with pepper, and sauté until the chicken in just browned but not fully cooked, stirring occasionally, approximately 5 minutes. Transfer the chicken to a platter.
Add the remaining 1-1/2 tablespoons of oil to the pan. Add the onion and sauté until the onion starts to soften, about 3 minutes.
Stir in the garlic and cubanelle pepper slices. Continue to sauté until the aromatics and peppers have softened and are fragrant, approximately 5 minutes.
Bring a large pot of well-salted water to a boil. Drop the pasta in the water and cook according to the package directions.
While the pasta is cooking, add the tomatoes, cherry peppers, and browned chicken to the pan. Bring this to a rolling simmer. Reduce the heat to medium-low and cook the sauce for about 10 to 15 minutes until the chicken is cooked through and the sauce is the desired consistency.
Stir the cream into the sauce and allow it to come back to a simmer for just a couple of minutes.
Transfer the pasta to the sauce using a spider or slotted spoon, allowing some of the pasta water to drip into the sauce.
Stir to coat the pasta well. If the sauce is too thick, add some more pasta water. Season with salt and pepper to taste.
Spoon the pasta and chicken mixture into a serving bowl or individual bowls. Sprinkle with parmesan cheese and garnish with basil, if using. Serve immediately and enjoy.