Give the potatoes a good scrub under cold water, but leave those skins on — they'll wrinkle beautifully and protect the flesh during cooking. Choose potatoes that are roughly the same size so they cook evenly.
Drop the potatoes into a heavy-bottomed pot and add just enough water to cover them by an inch. Stir in the coarse salt — it should taste like seawater. This salty bath is what creates the signature wrinkled skin and seasons the potatoes through and through.
Bring the water to a rolling boil, then dial the heat back to maintain a steady simmer. The potatoes are done when a knife slides through the largest one without resistance — usually about 20 minutes, but it depends on size.
⏱ 20 min
While the potatoes bubble away, grab your mortar and pestle. Crush the garlic cloves with the fine salt until you have a smooth paste — the salt acts like sandpaper to break down the garlic fibers.
Work both paprikas and the cumin into the garlic paste, grinding until the mixture turns deep red and releases a heady, toasted aroma. This is where the mojo gets its character — don't rush this step.
Drizzle in the vinegar first, stirring to loosen the paste, then slowly stream in the olive oil while whisking constantly. The sauce should emulsify into a thick, glossy mixture that coats the back of a spoon.
Once the potatoes are tender, drain them well and return them to the pot. Set it over low heat and shake the pot gently for about 2 minutes — this evaporates any remaining moisture and helps create those distinctive wrinkled skins.
⏱ 2 min
Transfer the wrinkled potatoes to a serving platter while they're still steaming hot. Serve the mojo sauce in a separate bowl for dipping — each person can control how much fire they want with each bite.