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1
Place the garlic, mustard, and egg in a food processor fitted with a blade attachment.
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2
Process until evenly combined, about 5 seconds.
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3
With the motor running, slowly add the olive oil in a thin stream, followed by the vegetable oil, until completely combined and thickened, about 5 minutes.
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4
Stop the processor, add the lemon juice, anchovy, paprika, and cayenne, and season with salt.
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5
Pulse until thoroughly mixed, about 10 (1-second) pulses.
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6
Stop and scrape down the sides of the bowl with a rubber spatula, then pulse again until all of the ingredients are evenly incorporated.
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7
Refrigerate for at least 2 hours to let the flavors mellow and meld, or refrigerate in a container with a tightfitting lid for up to 3 days.
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8
Heat the oven to 400 degrees F and arrange a rack in the middle.
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9
Place the potatoes on a baking sheet and prick each one once or twice with a fork.
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10
Drizzle with the oil, sprinkle with the measured salt, and toss to combine.
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11
Bake until easily pierced with a knife, about 30 minutes.
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12
Let cool on the baking sheet until cool enough to handle, about 10 to 15 minutes.
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13
Cut the potatoes in half and return them to the baking sheet cut-side up.
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14
Using your fingers, gently squeeze the sides of each potato half to slightly break apart the flesh.
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15
Season with salt and set aside to cool to almost room temperature, about 30 minutes.
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16
(Do not put the aioli on the hot potatoes or it will melt and drip off.)
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17
Just before assembling, mix the pimientos and salt in a small bowl.
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18
Dollop the potato halves with 1 teaspoon of the aioli each and divide the pimientos over the tops.
