Step 1

Heat 1 tablespoon olive oil in a small saucepan over medium heat until shimmering. Add 1 bay leaf, 1 teaspoon smoked paprika, 1/2 teaspoon cayenne pepper, and 1/2 teaspoon kosher salt. Carefully pour in 1 (15-ounce) can tomato purée and stir to combine. Bring to a boil. Reduce the heat to maintain a gentle simmer, then simmer until thickened, about 45 minutes. (This is a good time to make the alioli and cook the potatoes.) Remove the pan from the heat and stir in 1 tablespoon sherry vinegar.

Step 2

Finely grate 4 garlic cloves into a small bowl. Add 1 tablespoon freshly suqeezed lemon juice and stir to combine. Let sit for 30 minutes. Add 1 cup mayonnaise and 1 tablespoon extra-virgin olive oil, and stir to combine.

Step 3

Peel and cut 2 pounds russet potatoes into 1-inch pieces. Place in a medium saucepan and add enough cold water to cover by 1 inch. Bring to a boil over high heat. Boil until the potatoes are tender, about 7 minutes. (Do not overcook or they will fall apart.) Drain, then transfer to a kitchen towel and arrange the potatoes into a single layer to dry thoroughly.

Step 4

Heat 1 quart vegetable oil in a deep fryer or a large Dutch oven over medium-high heat until 350°F. Working in batches so as to not overcrowd the pot (there should be some space between each potato), use a spider or slotted spoon to add the potatoes to the oil. Fry, stirring occassionally, until the potatoes are golden-brown and crisp, 6 to 8 minutes. Transfer the potatoes to a paper towel-lined bowl to drain briefly, then transfer to a serving dish.

Step 5

Sprinkle 1 tablespoon smoked paprika and 1/4 teaspoon kosher salt over the potatoes and toss to coat. Serve with the alioli and bravas sauce for dipping.