Cook the pasta. Bring a large pot of water to a rapid boil, then season generously with a few tablespoons of Kosher salt. Add pasta, then cook according to package directions until al dente, about 11 minutes. Reserve about ½-1 cup of cooking water, then drain pasta in a colander.
Season the chicken. Place chicken in a large mixing bowl, then season with 2 tsp dried oregano, 2 tsp Kosher salt, ¼ tsp black pepper. Toss well to thoroughly coat.
Brown the chicken. Heat 3 Tbsp olive oil over medium-high heat in a large skillet with deep sides. When hot, add seasoned chicken and cook for 7-10 minutes, stirring occasionally, until the chicken is browned on all sides and fully cooked through. Use a slotted spoon to transfer chicken to a plate or bowl.
Sauté aromatics. To the same skillet, heat an additional 3 Tbsp olive oil in the skillet (or even better, 3 Tbsp sun dried tomato oil). When hot, add 3 cups chopped basil, then cook, stirring occasionally, until very fragrant, about 1 minute. Add 4 chopped garlic cloves, ⅓ cup sun dried tomatoes, and ¼ tsp crushed red pepper flakes, then stir and cook for an additional 1-2 minutes.
Make the sauce. Add 3 Tbsp tomato paste, then use a spoon to break up and dissolve. Add ½ cup white wine, then allow to cook off for 1-2 minutes. Pour in 1½ cups of heavy cream, then use the spatula to scrape the bottom of the pan and stir well.
Finish with the pasta. Add the cooked, drained pasta to the sauce, along with the chicken, 3 oz spinach, ½ cup of reserved pasta water, and ½ cup grated Parmesan. Stir well, add a bit more pasta water if wanted, then taste and adjust seasoning if needed. Serve in large bowls with additional grated Parmesan and basil leaves. Sprinkle each bowl with a pinch of flaky sea salt, then serve immediately!