Bring a large pot of water to a rapid boil, then season generously with Kosher salt. Add pasta, then cook according to package directions until al dente. Reserve about ½-1 cup of cooking water, then drain pasta in a colander.
Place raw jumbo shrimp in a large bowl. Season with blackening blend. Toss well to thoroughly coat.
Add tomato paste, then use a spoon to break up and dissolve. Pour in heavy cream, then use the spatula to scrape the bottom of the pan and stir well.
Add the cooked, drained pasta to the sauce, along with about reserved pasta water and 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!