For the ribs: Preheat the oven to 250 degrees F and get the ribs started first.
Mix together the salt, pepper and paprika. Remove the thin membrane from the bone side of the ribs and discard. Lightly sprinkle the seasoning over both sides of the ribs then place the racks, rib-side down on a baking tray. Place in the oven and bake until the ribs have a nice crust (also known as "bark") on the outside and the meat will be pulling away from the bone, 3 1/2 to 4 hours.
Meanwhile, prepare the romesco sauce: Set a large saucepan over medium heat and coat with a generous amount of olive oil. Add the bread cubes and toast until golden, 6 to 7 minutes. Season with some salt and toss the bread cubes as they cook so they brown evenly all over. When done, remove from the pan and set aside. Add the almond slivers to the dry pan and toast until golden, 3 to 4 minutes. Remove from the pan and set aside. Coat the pan with more olive oil and add the garlic and saute until fragrant, 1 minute. Add the drained red peppers and saute for 2 to 3 minutes. Then add the tomatoes. Season with more salt and the cayenne pepper. Bring to a boil, and then reduce the heat and simmer until the liquid has slightly reduced, 8 to 10 minutes. Remove from the heat and allow to cool.
To a food processor, add the almonds and the tomato and bell pepper mixture. Pulse until well chopped, and then add the bread cubes and continue to process. Add the sherry vinegar and, while the processor is running, drizzle in 1/2 cup olive oil. Continue to blend until the sauce has emulsified. Taste the sauce and season once more with salt if needed.
Remove the ribs from the oven, and while still hot, squeeze some fresh lime juice all over the racks. The ribs will absorb the lime juice and this will complement the rich, fatty spare ribs perfectly. Cut the ribs at every second bone and serve with the romesco sauce on the side.
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