Heat olive oil in a large pot over medium-high heat. Add the beef or lamb cubes and brown on all sides for about 5-7 minutes. Remove the meat and set aside.
In the same pot, add onions and garlic, sautéing until the onion is translucent (about 3-4 minutes).
Add the grated carrot and chopped bell pepper, cooking for an additional 3 minutes to soften the vegetables.
Return the browned meat to the pot, then pour in the diced tomatoes and broth. Add oregano, thyme, salt, and pepper. Stir everything together.
Bring the mixture to a boil, then reduce the heat and cover the pot. Let it simmer for 45 minutes, allowing the flavors to meld together.
After 45 minutes, add the orzo pasta to the pot, stirring gently. Cover and cook for an additional 10-12 minutes until the orzo is tender and has absorbed most of the liquid.
Once cooked, stir in half of the feta cheese and let it melt slightly into the mixture.
Serve hot, topped with the remaining feta cheese and a sprinkle of freshly chopped parsley.
Notes
Feel free to substitute the meat with chicken for a lighter version.