Combine the potatoes, 2 of the garlic cloves, the peppercorns and 1 teaspoon salt in a medium pot. Cover with cold water and bring to a boil. Reduce the heat to a simmer and cook until the potatoes are just tender when pierced with a thin knife, 12 to 15 minutes. Drain and cool until still warm but no longer hot.
Meanwhile, heat the oil in a medium pan over medium-high heat. Slice the remaining 2 garlic cloves and add to the oil along with the bread pieces. Cook, stirring, until the bread is golden, about 3 minutes. Transfer to the bowl of a food processor and add the red peppers, vinegar, smoked paprika, tomatoes and 3/4 teaspoon salt. Puree until smooth.
Heat a non-stick pan over medium-high heat until very hot. Cook the Serrano until crispy, turning, 2 to 3 minutes. Transfer to a paper towel-lined plate to drain and then break into small pieces.
To serve: Halve the warm potatoes and scoop out a small bit of the insides using a 1/4-teaspoon measure. Top the halves with a bit of the romesco sauce, sour cream, crispy Serrano shards and a sprinkle of parsley.