Heat 3 tablespoons olive oil in a large skillet over medium heat; cook and stir fresh tomatoes, onion, and garlic in the hot oil until onion is tender, 1 to 2 minutes. Stir canned tomatoes and tomato paste into the tomato-onion mixture, breaking down the whole tomatoes with a fork. Mix basil, salt, and pepper into the tomato mixture; simmer until liquid has slightly reduced, 15 minutes.
Stir vodka into the tomato mixture; simmer vodka sauce until slightly reduced, 15 minutes. Stir cream into vodka sauce and cook until heated through, 15 minutes.
Bring a large pot with lightly salted water and 1/2 teaspoon olive oil to a boil. Cook pasta, stirring occasionally, at a boil until tender yet firm to the bite, about 10 minutes; drain. Fold pasta into vodka sauce to coat.
