Patatas Bravas With Aioli

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1. 1Step 1: For the Salsa Brava: In a 3-quart saucepan, heat oil over medium heat until shimmering. Add onion and garlic, season lightly with salt, and cook, stirring frequently, until onion is softened and just beginning to brown on the edges, 5 to 7 minutes.
2. 2Step 2: Reduce heat to medium-low. Add sweet and hot pimentón, stir to combine, and cook until fragrant, about 30 seconds. Add tomato paste, and cook, stirring constantly, until tomato paste turns dark brick red, about 30 seconds. Add flour and cook, stirring constantly, until thoroughly combined and mixture begins to stick to bottom of saucepan, 30 seconds to 1 minute.
3. 3Step 3: Add stock, stir to combine, and bring to a boil over medium-high heat. Cook, stirring frequently with a heat-resistant spatula to prevent sticking and scorching, until mixture is thickened and coats the back of a spoon, 1 to 2 minutes. Transfer mixture to a countertop blender or immersion blender jar, along with sherry vinegar. Blend on high speed until completely smooth, about 1 minute. Season with salt to taste. Transfer to a bowl or airtight container (or a pastry bag or squeeze bottle if you prefer a precise drizzle), cover with plastic, pressing plastic wrap against the surface of the sauce to prevent a skin from forming, and set aside until ready to use. (Once sauce has cooled to room temperature, it can be refrigerated for up to 5 days.)
4. 4Step 4: For the Potatoes: Place potatoes in a large saucepan or pot and cover with 2 quarts (1.9L) water. Add vinegar and 2 tablespoons salt and bring to a boil over high heat. Cook until potatoes are tender and offer little resistance when poked with a paring knife, about 7 minutes. Drain and set aside.
5. 5Step 5: In a 12-inch cast iron straight-sided sauté pan or large Dutch oven, heat oil to 350°F (175°C). Add potatoes in single layer and cook, shaking the pan and flipping the potatoes with a slotted spatula or tongs occasionally, until golden brown and crisp, 5 to 7 minutes. Remove from heat. Using slotted spoon or wire-mesh spider, transfer potatoes to a paper towel-lined bowl. Season to taste with salt and pepper.
6. 6Step 6: For Serving: Transfer potatoes to a large serving dish or divide between individual plates, drizzle with salsa brava and allioli, and serve, passing extra salsa brava and allioli at the table.