To begin, soak the chickpeas overnight in a large bowl of water, covering them well to allow expansion. Drain and rinse before use.
In a large, heavy pot, combine the beef shank, pork belly, ham hock, and chickpeas. Add enough water to cover the ingredients, then bring to a gentle boil. Skim off any foam that rises to the surface to ensure a clear broth.
Reduce the heat to a simmer and add the carrots, potatoes, and leek. Season with salt and pepper to taste. Cover partially and let it cook for about 2 hours, until the meat and chickpeas are tender. Add more water if necessary to keep ingredients submerged.
After 2 hours, add the cabbage quarters to the pot. Let them cook for about 20-30 minutes until softened but still holding their shape.
In a separate small saucepan, bring water to a gentle boil. Place the chorizo and morcilla in the saucepan, allowing them to cook through for about 15-20 minutes. This prevents the strong flavours from overpowering the broth.
Once the chorizo and morcilla are cooked, carefully add them to the main pot with the stew. Simmer for an additional 10 minutes to allow the flavours to meld, then remove from heat.
Using a slotted spoon, remove the meats and vegetables from the pot and arrange them on a large serving platter. Drizzle with a bit of olive oil and sprinkle with extra salt if needed.
Serve Cocido Madrileño in three traditional courses: Begin with the flavourful broth, strained and served as a soup. Follow with the chickpeas and vegetables as the second course, and finish with the meats as the final course. Accompany each course with rustic bread, and for an authentic touch, serve with pickled peppers for a hint of acidity that complements the rich flavours.