Cut the Potatoes into bite-sized cubes (about 2–3 cm). Rinse, then parboil in salted water (add a pinch of Salt) for 5–7 minutes until just tender; drain and let steam-dry so they lose excess moisture.
Heat a generous splash of Olive Oil in a large skillet over medium-high heat. Fry the potatoes in batches without overcrowding until crisp and golden on all sides, about 6–8 minutes per batch. Transfer to a paper towel-lined tray and season lightly with Salt.
Make the bravas sauce: lower the heat and warm 2 tbsp more Olive Oil in a saucepan. Add finely chopped Onion and cook until translucent, then stir in minced Garlic and cook 30–60 seconds until fragrant.
Stir in the Sweet Spanish Paprika and Hot Spanish Paprika to toast briefly, then add the Crushed Tomatoes, Chicken Stock, a splash of Sherry Vinegar, a pinch of Sugar and a little extra Salt. Simmer gently 12–15 minutes until thickened and flavorful. Taste and adjust vinegar, sugar, or salt as needed.
If you prefer a smoother sauce, blitz briefly with a hand blender or in a food processor until velvety; keep warm.
Prepare the garlic aioli: in a small bowl whisk the Egg Yolk with a little Lemon Juice. Very slowly drizzle in Light Olive Oil while whisking vigorously to form a thick emulsion. Stir in finely minced garlic, season to taste with Salt and more lemon if desired.
To serve, toss the hot potatoes with some of the bravas sauce so they are coated, pile onto a serving plate, spoon extra sauce over the top and finish with dollops of the garlic aioli. Serve immediately while crispy.
