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1
Warm a generous measure of olive oil in a heavy pot over low-to-medium heat. Add the sliced leeks — white and pale green parts only; discard the dark green tops entirely. Sweat, stirring occasionally, for 15–20 minutes until completely soft, translucent, and almost melting. The leeks must yield no resistance and carry no raw edge.
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2
Add the diced potato and pour over the water or light stock (for the bacalao version, use the soaking liquid in place of or alongside the water). Season with salt. Bring to a gentle simmer and cook until the potato is fully tender and beginning to break down at its edges, thickening the broth slightly.
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3
If making the bacalao version, remove the pot from direct heat. Add the desalted shredded salt cod and leave to finish in 5 minutes of residual heat. The cod should be just set — opaque throughout and barely fibrous.
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4
Taste and correct the salt. Ladle into warm bowls. Finish each portion with a drizzle of good olive oil. Serve with a slice of warm Idiazábal alongside.