Soak the potatoes in cold water for 30 minutes.
Place 2 cloves of the minced garlic on a cutting board and sprinkle with 1/4 teaspoon of the salt.
Mash the garlic with the flat side of a knife blade until a smooth paste forms.
Transfer the garlic paste to a small bowl.
Whisk the mayonnaise, the lemon juice, and 1 tablespoon of the olive oil into the garlic paste until it is smooth.
Cover the garlic mayo sauce and refrigerate it until ready to serve.
In a small saucepan, heat 2 tablespoons of the olive oil over medium heat.
Add the onion to the oil and cook, stirring, until it is tender, about 2-3 minutes.
Add the remaining minced garlic to the onion and cook until it is fragrant, about 1 minute.
Stir the flour, the sweet paprika, and the hot paprika into the onion mixture until it is smooth.
Gradually stir the chicken broth into the onion mixture.
Add the bay leaf to the onion mixture and bring it to a boil.
Cook the bravas sauce, stirring constantly, until it has thickened, about 6-8 minutes.
Transfer the saucepan from the heat and allow the bravas sauce to cool slightly.
Discard the bay leaf.
Using an immersion blender, purée the bravas sauce.
Return the bravas sauce to the heat and cook until it is heated through. Keep the sauce warm.
Drain the potatoes and pat them dry with paper towels.
In a deep-fat fryer or an electric skillet, heat the remaining oil to 250 degrees F.
Fry the potatoes until they are tender, about 8-10 minutes.
Transfer the fried potatoes to paper towels to drain and cool completely.
Increase the heat of the oil to 375 degrees F.
Fry the potatoes again, turning them frequently, until they are crisp and golden-brown, about 3-4 minutes.
Drain the potatoes on paper towels.
Sprinkle the potatoes with the remaining salt while they are still hot to make sure it adheres.
Serve the potatoes with the garlic mayo and the bravas sauce.