To prepare the bravas sauce, in a saucepan over medium heat, warm 3 Tbs. of the olive oil. Add the onion and cook, stirring occasionally, until softened, about 5 minutes. Add the garlic and cook, stirring occasionally, until fragrant, about 1 minute. Season with a big pinch of salt, then add the smoked paprika, hot paprika and tomato paste and stir to coat. Cook, stirring for 1 minute to toast the tomato paste slightly. Sprinkle with the flour and stir to coat, then cook for 1 minute to eliminate the raw flour taste. Slowly add the stock, stirring constantly until combined. Cook, stirring occasionally, until the flavors come together, about 2 minutes. Add the sherry vinegar and remove from the heat.

Transfer the mixture to a blender and blend on high speed until smooth, about 2 minutes, pouring in the remaining 2 Tbs. olive oil to emulsify the sauce. Taste and adjust the seasoning with salt. Transfer to a bowl and set aside. Wash and dry the blender container.

To prepare the alioli, with the blender running, drop in the garlic cloves and process on medium-high speed until minced. Add the egg and egg yolk, the lemon juice and a big pinch of salt and blend until combined. Stop the blender and scrape down the sides. With the blender running, slowly pour in the canola oil and olive oil and blend until emulsified, about 30 seconds. Taste and adjust the seasoning with salt. Set aside.

To prepare the put the in a and add cold water to cover. Add the and 2 1/2 Tbs. and bring to a boil over medium-high heat. Reduce the heat to and simmer until the are very fork-tender and ragged on the outside (the will help achieve this texture), about 12 minutes. Drain the very well.