Place the ribs in a large pot with the whole head of garlic (cut in half), carrot (roughly chopped), celery, thyme, bay leaves, and peppercorns. Cover completely with water and bring to a boil.
Once boiling, reduce heat to low and simmer gently for 1.5 hours until the meat is fork-tender (easily pierced with a fork).
While the ribs cook, make the glaze: In a small saucepan, melt the quince paste with the vinegar and water over medium heat. Simmer until the mixture thickens to a glaze consistency.
Remove the ribs from the cooking liquid and pat them completely dry with paper towels. Season generously with salt and pepper on both sides.
Preheat your grill to medium heat (350°F/175°C). Grill the ribs for 10-15 minutes, turning frequently and basting with the quince glaze each time you turn them.
Serve the ribs hot with extra glaze on the side for dipping.
