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For the potatoes:
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1. Place the potatoes in a medium saucepan and cover with water until the potatoes are submerged. Add vinegar and salt and bring to a boil. Cook the potatoes until they are tender (about 7 minutes). Drain and set aside.
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2. Heat oil in a saute pan over medium-high heat until it registers 350 F (175 C) on a thermometer. Add the potatoes in a single layer and cook, shaking the plan and flipping the potatoes occasionally until they are golden brown and crisp (approximately 5 minutes). Once cooked, transfer the potatoes with a slotted spoon to a plate lined with paper towels. Season to taste with salt and pepper and both sauces (recipes listed below).
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For the garlic aioli:
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1. Put the garlic, egg yolk, lemon juice, honey and salt in a bowl and whisk together.
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2. Slowly drizzle in the olive oil while whisking until you have a thick pale yellow emulsion.
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For the tomato sauce:
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1. Slice the tomatoes in half. Place a grater over a bowl and rub the open side of the tomato over the grater until all the flesh is grated. Discard the skins. Strain the grated flesh through a sieve to produce approximately 1 1/2 cups of tomato puree.
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2. Pour the olive oil into a small saute pan and warm over low heat. Add the tomato puree, sugar, bay leaf, pimenton and cayenne. Raise the heat to medium and cook until the mixture reduces by a quarter and becomes a deep red color (approximately 10 minutes).
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3. Remove from the heat, add the vinegar and season to taste with salt.
