Heat 2 tablespoons olive oil in a large Dutch oven or heavy pot over medium-high heat.
Add the chopped onion, finely chopped celery, and chopped carrot and sauté for 7–8 minutes until softened.
Add the ground turkey and minced garlic; cook 5–7 minutes more, breaking up the meat, until the turkey is browned.
Stir in the crushed tomatoes, 1/2 tablespoon Worcestershire sauce, 1/2 teaspoon Italian seasoning, 1/2 teaspoon dried oregano, 1/2 teaspoon salt, and 1/4 teaspoon red pepper flakes.
Reduce heat and simmer the sauce, partially covered, for about 15 minutes, stirring occasionally.
Meanwhile, bring a large pot of salted water to a boil and cook 16 ounces tortiglioni according to package directions until al dente; drain, reserving a small cup of pasta water if needed.
Stir 1/2 cup heavy cream and the torn basil into the sauce and warm through; add a splash of reserved pasta water if you want a looser sauce.
Taste and adjust seasoning with black pepper and more salt if needed, then toss the drained pasta with the sauce.
Serve with freshly grated Parmesan cheese if desired.