Blanch the ribs in boiling water for 5-8 minutes. Rinse under cold water to cool. Set aside.
Heat a large frying pan with 1 tablespoon oil over high heat. Stir-fry the garlic until fragrant, 2-3 minutes. Stir in the ribs with the black soy sauce and soy sauce.
Stir in the shaoxing wine and slab sugar, mix well. Add enough water to cover 3/4 of the ingredients. Simmer for 3 minutes over high heat. Stir to ensure the sugar slab has dissolved.
Reduce the heat to medium-low, cover, simmer for 40 minutes. Stir in the black vinegar, simmer for 5 minutes.
Transfer the ribs onto a serving plate, keeping the sauce in the frying pan. Thicken with the cornflour slurry. Once thick, pour over the ribs and serve.
Slab sugar is compressed brown sugar in blocks. It's also known as brown sugar in pieces. You will find sugar slabs, along with shaoxing wine, black soy sauce and Chinese black vinegar in Chinese/Oriental speciality stores.