Heat the olive oil in a large skillet over medium heat. Add the chopped onion, garlic, carrot, and celery. Cook until the vegetables soften—about 6 to 8 minutes.
Stir in the ground turkey, breaking it apart with a wooden spoon. Cook until browned and no longer pink.
Mix in the tomato paste, canned tomatoes, oregano, paprika, Worcestershire sauce, salt, and pepper. Simmer uncovered for 15 minutes, stirring occasionally.
While the sauce simmers, preheat your oven to 375°F (190°C).
Add the gnocchi and chicken broth to the skillet, stirring gently to coat everything in the sauce.
Transfer the mixture to a lightly greased baking dish. Sprinkle the grated mozzarella evenly over the top.
Bake uncovered for 20 minutes or until the cheese is melted and bubbling. Garnish with chopped parsley before serving.