Heat olive oil in a frying pan over medium-low heat. Add the pepper and onion and cook, stirring infrequently, until they're soft and caramelized, about 20 to 25 minutes.
Once the peppers and onions are caramelized, add the garlic and cook until fragrant, about 30 seconds. Deglaze the pan with water and stir in the cayenne and paprika.
Simmer for 3 to 5 minutes to help the flavors infuse.
Transfer the contents of the pan to a food processor. Add the extra virgin olive oil and red wine vinegar, and pulse until smooth. Season with salt to taste and set aside.
Patatas Bravas
While the peppers and onions are caramelizing, heat a quarter- to a half-inch of vegetable oil in a deep cast iron pan.
Once the oil is hot, add the potatoes and fry them until browned and crispy, about 20 to 25 minutes. Stir infrequently at first, but more frequently as they begin to crisp to ensure even browning.
Remove the potatoes from the oil with a slotted spoon or spatula, and transfer to a cooling rack positioned over paper towels to drain. Sprinkle with a pinch of salt.
When the sauce is done and you're ready to serve the patatas bravas, add the sauce and light mayo to a frying pan over low heat. Stir to combine until the sauce is smooth and silky, then add the potatoes.
Stir gently to coat the potatoes in the sauce. Continue cooking until the potatoes and sauce are warmed through. This will only take a minute or two if the sauce and potatoes were freshly made. If you made the sauce ahead of time, this may take 5 to 10 minutes.
Transfer the patatas bravas to a serving dish and drizzle with garlic aioli. Serve hot.
Notes
Make ahead notes: You can make the patatas bravas sauce ahead of time and store it in the fridge for up to 5 days in an airtight container. This is especially useful if you're hosting a tapas party and want to make prep work a little easier the day of!Storing and reheating leftovers: Store leftovers in an airtight container in the fridge for up to 5 days. Reheat in the microwave for 1 to 2 minutes, then add a fresh drizzle of garlic aioli before serving.Serving suggestions: Patatas bravas is an authentic Spanish tapas dish, which means it's a small plate that can be served with other small plates as a meal. We love pairing it with Spanish baked goat cheese in tomato sauce and chorizo potato skewers. Check out our blog post above for more suggestions!This recipe also makes a perfect appetizer or side dish for two. It's great for date nights at home, especially if you enjoy cooking together.