Bring a large pot of water to a rolling boil and add a generous amount of Kosher salt. Cook the rigatoni according to package directions until al dente, about 11 minutes. Before draining, reserve about 1 cup of the starchy cooking water. Drain the pasta in a colander and set aside.

In a large bowl, combine the chicken pieces with dried oregano, 2 teaspoons Kosher salt, and 1/4 teaspoon black pepper. Toss well to coat evenly.

Heat 3 tablespoons olive oil in a large, deep skillet over medium-high heat. Once shimmering, add the seasoned chicken and cook, stirring occasionally, until browned on all sides and cooked through, about 7 to 10 minutes. Use a slotted spoon to transfer the chicken to a plate or bowl.

Reduce the heat to medium and add the remaining 3 tablespoons olive oil (or sun-dried tomato oil) to the same skillet. Stir in the chopped basil and cook until fragrant, about 1 minute. Add the minced garlic, chopped sun-dried tomatoes, and crushed red pepper flakes; cook for another 1 to 2 minutes, stirring frequently.

Add the tomato paste and stir to dissolve and incorporate. Pour in the white wine and let it bubble for 1 to 2 minutes, scraping up any browned bits from the bottom of the pan. Whisk in the heavy cream, then stir until the sauce is smooth and slightly thickened.

Add the cooked pasta, cooked chicken, baby spinach, 1/2 cup reserved pasta water, and grated Parmesan to the skillet. Toss everything gently to combine, adding more pasta water a little at a time if the sauce seems too thick. Taste and adjust seasoning with salt and pepper if needed. Serve in warm bowls, topped with extra Parmesan, fresh basil leaves, and a pinch of flaky sea salt.