Heat the olive oil in a large pot over medium heat. Add the ground turkey, onion, and garlic. Cook for 6 to 8 minutes, breaking up the turkey until it is browned and the onion softens.
Stir in the tomato sauce, oregano, salt, and black pepper. Let the mixture simmer for 5 minutes so the flavors blend.
Add the spiralized zucchini noodles to the pot. Cook for 3 to 4 minutes, stirring gently, until the noodles are just tender.
Remove the pot from the heat. Sprinkle the Parmesan cheese and fresh parsley over the top before serving.