To make the dipping sauce, using a mortar or food processor, make a paste with the garlic, ½ tsp smoked paprika, and a pinch of salt
To this paste, add mayonnaise, sherry vinegar, tomato paste, a pinch of cayenne, and chipotle chili powder. Mix until well combined, cover, and refrigerate
Make the spice mix for sprinkling over fried potatoes. In a small bowl, mix 1 tbsp salt, ½ tsp smoked paprika, ½ tsp chipotle chile powder, and pepper to taste. Set aside for later.
Prepare your cooking broth for potatoes: measure 1 tbsp salt, 1 tsp smoked paprika, cumin, and bay leaves, and add to a medium pot with 2 quarts of water
Heat 2 cups of oil in a medium-sized skillet and fry potatoes until golden brown. Place fried potatoes in a paper towel-lined plate and sprinkle with the reserved spice mix.
Bring broth to a boil and add potato cubes. Cook for 5 to 6 mins, just until a bit tender but not fully cooked. Strain and let potatoes cool completely.