Choose a large deep walled skillet with a tight-fitting lid or a Dutch oven with lid. Heat over medium-high heat and add the oil then the onion. Cook the onion for a few minutes until soft and translucent. Add the garlic and cook another minute or so until fragrant.
Add the ground beef and combine well with the onion and garlic, breaking up the beef and cooking until browned through.
Add the paprika, salt, pepper, mint, oregano, thyme, cinnamon, and orzo and mix well. Toast the spices and the orzo for a couple of minutes. Next, add the tomato sauce, diced tomatoes, and beef broth and stir to combine. Place the lid on and let simmer over medium heat for 5-7 minutes.
Check to see if the orzo is cooked through. If it still has a bite to it, return lid and let simmer a few more minutes, adding ½ cup more liquid (water or broth) only if necessary. Taste and adjust seasoning if needed.
Stir in the apple cider vinegar and the spinach and stir until the spinach has wilted in.
Taste and adjust seasoning if needed. Serve with feta garnished on top.