Use a mortar and pestle to mash the garlic and salt into a paste. In a small bowl, whisk together yolk and lemon juice. Add the oil in a thin, steady stream, whisking constantly until the mixture is emulsified and smooth. If the mix separates, stop adding oil and continuing whisking until it comes together, then continue adding oil. Whisk in garlic paste and season with salt and pepper. Keep refrigerated.
Add oil to a saucepan and sauté onions over medium heat until soft. Add the garlic and cook until fragrant. Stir in vinegar, tomatoes, peppers, paprika, and salt. Cook until the tomatoes begin to break down, about xx minutes. Remove from heat and, using a hand mixer, puree the sauce until smooth.
Preheat the oven to 400°Toss the potatoes in a bowl with olive oil, salt, and pepper until well coated. Spread the potatoes in a single layer on a sheet pan and roast in the oven for 30-45 minutes or until browned and crispy. Flip halfway through cooking for even browning. Serve with generous amounts of brava and alioli sauce and top with a dash of hot smoked Spanish paprika.