Heat oil in a large saucepan over medium heat. Add onion and tomato paste and cook, stirring occasionally, until onions are softened, about 3 minutes.
Add sweet chili rub, stirring constantly, until fragrant, about 30 seconds
Stir in tomatoes and 1/2 teaspoon salt. Add vodka and simmer briskly on medium-high heat until alcohol flavor is cooked off, 8 to 10 minutes; stir occasionally.
Stir in cream and cook until hot, about 1 minute.
Add pasta and toss over medium heat until pasta absorbs some of the sauce, 1 to 2 minutes. Stir in parsley and adjust seasoning with sea salt. Divide among pasta bowls and serve immediately, finishing with cheese.