Heat the oven to 400°F. Lightly oil a 9×13-inch baking dish.
In a small saucepan, combine the chicken broth and tomato soup with the oregano and red pepper flakes. Bring just to a simmer over medium heat, then turn off the heat. Warming the liquid helps the orzo cook evenly.
Add the dry orzo, olive oil, garlic, and sun-dried tomatoes to the prepared baking dish. Toss to coat and spread the orzo in an even layer.
Pour the hot tomato-broth mixture over the orzo and stir to ensure all the pasta is submerged. Nestle the frozen meatballs evenly over the top.
Cover the dish tightly with foil and bake for 18 minutes.
Uncover, stir well to loosen any orzo from the corners, and fold in the chopped spinach. Return to the oven uncovered and bake for 10–12 minutes, until most of the liquid is absorbed and the orzo is tender.
Sprinkle the Parmesan evenly over the surface. Switch the oven to broil and broil for 2–3 minutes, just until the top is bubbly and lightly golden. (If you prefer not to broil, bake 3–5 more minutes instead.)
Let the bake rest for 5–8 minutes so the sauce settles. Taste and adjust seasoning if needed, then serve hot.