Preheat the oven to 375 degrees Fahrenheit.
Pierce holes in the potatoes with a sharp knife. Place on a plate and microwave on high for 2-3 minutes to soften. Cut into 1 inch pieces. Set aside.
In a 12 inch cast iron skillet heat 2 tablespoons of olive oil over medium heat. When it's hot add the onion, cook 3 minutes. Add the garlic cook another minute. Add the tomatoes and cook a few minutes until they begin to burst, stirring to soften them quicker.
In the bowl of a food processor add the mayonnaise, tomato paste, smoked paprika, Tabasco and sherry vinegar. Add the tomato mixture. Pulse until well combined.
In the same pot you cooked the onions in (do not rinse) add another 2 tablespoons of olive oil and cook the potatoes for 5 minutes until golden brown. Toss with tongs to make sure all sides cook. Transfer the potatoes to a baking sheet, place in a single layer and bake for about 10 minutes until crispy.
Place the potatoes back in the skillet, over low heat mix in the aioli. Continue to cook until warmed through.
Serve immediately topped with fresh parsley.
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