Heat olive oil in a large skillet over medium heat.
Add chopped onion and cook for 3 to 4 minutes until softened.
Add minced garlic and cook for 30 seconds until fragrant.
Add ground turkey to the skillet and cook, breaking it up with a spoon, until browned and cooked through, about 6 to 8 minutes.
Stir in dried oregano, dried thyme, salt, black pepper, and crushed red pepper flakes; cook for 1 minute.
Add orzo pasta to the skillet and stir to combine with the turkey mixture.
Pour in diced tomatoes with their juice and chicken broth; stir well.
Bring the mixture to a boil, then reduce heat to low and cover the skillet.
Simmer for 12 to 15 minutes, stirring occasionally, until the orzo is tender and most of the liquid is absorbed.
Remove the skillet from heat and stir in grated Parmesan cheese and chopped fresh parsley.
Adjust seasoning with additional salt and pepper if needed.
Serve hot.