Preheat the oven to 220°C / 430°F.
Pulse onion, garlic, and parsley into a small food processor until minced.
Combine the ground meat with the pulsed onion mixture, egg, vinegar, paprika, cumin, breadcrumbs, dried oregano, and thyme. Season with salt and pepper. Knead the mixture well, gradually adding 100 ml of water. You may need slightly less water. The mixture should be soft and moist but shapeable.
Drizzle a 30 x 20 cm (12 x 8 inches) baking dish or pan of similar size with olive oil.
Shape into 8 meatballs and place them in the baking dish. Toss in the allspice berries and bay leaves.
Bake the meatballs for 15 minutes to get some color on top. Then remove from the pan and set aside, covered, to keep warm.
Drop the heat to 200°C / 390°F.
Make an instant sauce. Whisk to combine tomato paste with tomato passata, hot water or stock, sugar, salt, and pepper.
Add the orzo to the baking dish and pour the instant sauce in.
Bake for 10 minutes. Remove from the oven and give a good stir.
Return the meatballs to the baking dish, with their roasted side facing down.
Bake for 20 minutes, stirring the orzo once halfway through baking (the orzo tends to stick to the sides). Don't flip the meatballs. Let them roast on top.
Take the baking dish out of the oven and raise the heat again to 220°C / 430°F.
Add the feta chunks here and there and give it a final roast for 5 minutes. If the orzo becomes too sticky, add a splash of water.
Serve while it's still hot with a generous sprinkle of freshly ground pepper and dried oregano.