Start by cooking the pasta. In a large pot, bring salted water to a boil and add 12 ounces of your choice of tube-shaped pasta such as rigatoni or mezzi rigatoni. Boil until the pasta is al dente, which should take about 8 minutes. Remember to reserve 1 cup of the pasta cooking water before draining the pasta.
Next, you’ll sauté the chicken. In a large oven-safe skillet, heat 1 to 2 tablespoons of extra-virgin olive oil over medium-high heat. Toss 1 pound of cubed boneless, skinless chicken breasts with 1 tablespoon of Italian seasoning, 1 teaspoon of paprika, 1¼ teaspoons of kosher salt, and ½ teaspoon of black pepper. Cook the chicken for about 8 minutes, stirring occasionally, until it is no longer pink and cooked through. Set the chicken aside on a plate.
In the same skillet, add the minced shallots and cook for about 3 minutes until they become soft and translucent. Then, toss in 4 cloves of minced garlic, a pinch of crushed red pepper flakes, 1 cup of thinly sliced jarred roasted tomatoes, and 2 to 3 handfuls of fresh baby spinach. Stir everything for about 2 to 3 minutes, until the spinach wilts and brightens in color. Season with the remaining kosher salt.
Stir in ½ cup of pesto and ½ cup of heavy cream into the skillet mixture. Next, add the drained pasta along with the reserved pasta cooking water, stirring well until the sauce thickens and coats the pasta evenly.
Incorporate the sautéed chicken and ⅓ cup of freshly grated Parmigiano-Reggiano into the pasta. Mix everything until well combined. Top the pasta with torn pieces of 3 to 4 ounces of fresh mozzarella and sprinkle the remaining Parmigiano-Reggiano over the top.
Place the skillet under the broiler for about 3 to 5 minutes, keeping a watchful eye as the cheese melts and turns golden brown. Once bubbling and beautifully browned, remove it from the oven, garnish with fresh basil, and serve hot.