Soak the chickpeas overnight in plenty of water with a handful of salt.

Rinse the meats, pork belly, and bones, and place them in a large (5-quart) pot. Cover with water and bring to a boil over high heat.

Once boiling, reduce the heat to medium and skim off any brown or white foam that forms on top to remove impurities from the meat and bones. Skim off any excess fat as well.

When there is little to no foam left (after about 30 minutes), add the drained chickpeas and wait for the pot to return to a boil.

Simmer for 2 hours, then add the carrots and potato.

After 30 minutes, cook the chorizo and blood sausage in a separate saucepan so the broth doesn't get too greasy. Depending on the chorizo, this will take 30 to 50 minutes.

Three hours after the pot first started boiling, remove and set aside the meats. Strain the chickpeas and add the noodles to the broth. Cook for 5 minutes.

Cocido Madrileño is traditionally served in three courses: 1st, noodle soup; 2nd, chickpeas; 3rd, meats and pork belly. But it's fine to mix them if you prefer!