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1
In a mortar, pound the garlic cloves to a smooth paste. Add the sweet and hot pimentón and work into the garlic until fully combined into a dense, fragrant picada. The paste should be cohesive and deeply coloured.
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2
Pour the olive oil into a cazuela or wide earthenware pot over medium heat. Add the picada directly to the oil and stir for no more than one minute — this is where the dish lives or dies: the pimentón must bloom in the oil to release its colour and depth without burning; the moment the paste turns from bright red to brick and the kitchen fills with a sharp, toasted paprika aroma, proceed immediately.
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3
Pour in the water and season with salt. Add the potato chunks. Bring to a steady simmer and cook until the potatoes begin to soften at the edges but are not yet cooked through — a knife tip meets resistance at the centre.
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4
Add the eel sections to the simmering broth. Cook, uncovered, until the eel is just opaque and pulls cleanly from the bone with gentle pressure — the flesh should not flake to mush. The broth remains loose, closer to a soup than a stew.
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5
Taste the broth and correct for salt. Serve the cazuela directly at the table, with white rice or crusty bread alongside.