Rinse the salt cod. Cover with plenty of cold water and refrigerate 24 to 48 hours, changing the water every 8 hours. Drain.
Place cod in a pot of fresh water, bring to a gentle simmer and cook about 10 minutes, until it flakes and reaches 145°F. Drain, remove skin and bones, and break into large flakes. Taste a small cooked piece to check the salt level.
Simmer the potatoes in water until just fork-tender, about 12 to 15 minutes; drain.
Heat olive oil in a wide pot over medium heat. Cook onion for 5 minutes, add garlic and cook 1 minute. Stir in crushed tomatoes and simmer 15 minutes.
Fold in cod, potatoes, olives, capers and chiles. Simmer gently for 10 to 15 minutes, adding water if needed. Taste before adding salt. Finish with parsley and serve with bolillos or warm tortillas.