Pat the lamb completely dry and season generously with salt and pepper. If time allows, season the evening before and refrigerate uncovered overnight.
Preheat the oven to 180°C (350°F). Heat 2 tbsp olive oil in a heavy Dutch oven over high heat and sear the lamb in batches, 3–4 minutes per side, until deeply browned. Do not crowd the pan. Set the lamb aside.
Reduce the heat to medium and add the remaining ¼ cup olive oil. Cook the diced onion until soft and translucent, add the garlic, then bloom the cinnamon, allspice, cloves, and bay leaves in the oil for a minute until fragrant.
Pour in the crushed tomatoes, scraping up the browned bits, then add the warm stock and the sugar if using. Season with salt and pepper and bring to a simmer.
Return the lamb to the pot, pressing the pieces into the sauce. Cover tightly and braise in the oven for about 2 hours, until the lamb is fork-tender.
Remove the pot, taste and adjust the seasoning, and check the liquid — it should roughly half-cover the meat; top up with warm stock if needed. Stir in the orzo and return to the oven, uncovered, until the orzo is tender and has drunk in the sauce, about 20–25 minutes.
Rest the giouvetsi for 10 minutes before serving — the orzo finishes absorbing as it sits. Serve showered with grated kefalotyri and parsley.