Heat a large skillet over a medium heat. Add butter, shallots, and chicken. Sauté until shallots are softened and chicken is no longer pink on the outside.
Add the garlic and continue cooking until shallots start to caramelize, about 2 to 4 minutes.
Add parsley, sea salt, tomato paste and pepper, and mix to form a paste. Lower the heat and cook for about 5 minutes, stirring occasionally
Add the vodka. Scrape bottom of pan with a wooden spoon and cook for about 5 minutes more.
Meanwhile, bring a medium pot of salted water to a boil. Cook pasta according to package directions.
When the pasta is cooked, transfer about 1 cup of the cooking water to a heat-proof measuring cup. Set aside. Drain the rest of the pasta.
Add the cream to the tomato sauce; reduce heat to low and simmer for about 3 minutes.
Add pasta to the sauce and mix to coat.
If the pasta sauce appears too thick, add some of the reserved pasta cooking water to “loosen it up” (I usually have to add about ½ cup)
Top with basil and season to taste with salt and pepper.