Heat the oven to 425 degrees Fahrenheit (220 degrees Celsius). On a rimmed sheet pan, toss 1 pint whole cherry tomatoes with 1 tablespoon olive oil, ¼ teaspoon kosher salt, and black pepper. Roast until blistered and jammy, 15–18 minutes; set aside.

Set a large skillet over medium-high heat. Add 12–16 ounces Italian sausage (casings removed) and cook, breaking into crumbles, until golden brown, 6–8 minutes. Transfer sausage to a plate; leave drippings in the pan. If the pan looks dry, add 1 tablespoon olive oil.

Lower to medium heat. Add 2 thinly sliced shallots and cook until translucent and sweet, 4–5 minutes. Stir in 2 minced garlic cloves and ½ teaspoon red pepper flakes; cook 30–45 seconds until fragrant.

Add ⅓ cup tomato paste and cook, stirring with a wooden spoon, until it turns deep brick red and leaves a fond on the pan, 2–3 minutes.

Pour in ½ cup dry white wine; scrape up browned bits and reduce 1–2 minutes. Stir in ⅔ cup chicken stock (add a splash more if needed) to loosen into a saucy consistency. Return the browned sausage and any juices; simmer 2 minutes.

Stir in ½ cup heavy cream and season with 1 teaspoon kosher salt and black pepper. Keep the creamy sauce warm on low heat.

Bring a large pot of water to a boil; salt it well. Cook 12 ounces paccheri until just al dente. Reserve 1 cup pasta water; drain.

Add the drained pasta to the sauce with about ½ cup reserved pasta water. Toss over medium heat 1–2 minutes until glossy and clinging. Off heat, fold in 1 cup finely grated Parmigiano-Reggiano and 2 tablespoons butter. Add more pasta water as needed for a silky, spoon-coating finish.

Spoon into warm bowls, top with the roasted cherry tomatoes, extra Parmigiano, and fresh basil if you like. Drizzle a touch of olive oil to serve.