Place the ground chicken in a bowl and season it with ¾ teaspoon kosher salt and a big pinch of pepper. Add a pinch of crushed red pepper.
Add the garlic, shallot, and basil leaves to a food processor and pulse until minced. Add the egg, heavy cream, and Italian seasoning. Pulse until blended. Add the breadcrumbs and Parmesan cheese and pulse until it forms a paste-like consistency.
Pour the mixture over the chicken and mix until just incorporated. If the mixture is too wet or doesn’t hold together, add a scant amount of extra breadcrumbs.
You can fry or microwave a tiny piece of the mixture to taste the seasonings if you like. Adjust the flavor of the mixture to your preferences.
Roll into 1-inch balls and transfer to a plate.
Fry the meatballs:
Add 2 tablespoons olive oil to a large, heavy-bottomed pot over medium heat. Once hot, add the meatballs in an even layer and cook for 2–3 minutes per side until browned. Cook in batches if needed to avoid overcrowding the pot. They do not need to be cooked through. Transfer them to a plate.
Make the sauce:
Return the heat on the pot to medium. Pour in the red wine and bring to a boil. Add the arrabbiata sauce, water, a pinch of sugar, and a big pinch of crushed red pepper. Taste and add salt if needed.
Simmer the meatballs:
Add the meatballs to the sauce and return it to boiling. Turn the heat down to low. Cover and simmer for 30 minutes. After 30 minutes, taste and adjust the seasonings.
Make the pasta:
Meanwhile, bring a large pot of salted water to a boil. Add the pasta and cook until al dente. Reserve ½ cup of the water and drain the pasta.
Finish the sauce:
Return the heat on the sauce to medium. Once it begins to bubble rapidly, add the pasta water and Parmesan cheese. Stir to melt the cheese into the sauce. Immediately add the cooked pasta and toss to coat for 1 minute. Turn off the heat.
To serve:
Spoon the pasta and meatballs onto plates. Garnish with more grated Parmesan cheese and a few basil leaves. Enjoy!