In a large pot, bring the bottled clam juice and water to a boil over high heat.

Carefully add the live lobsters headfirst into the boiling liquid.

Cover the pot and boil for 15 minutes or until the lobster shells are bright red and their tails are curled.

Remove the lobsters from the pot, reserving 2 tablespoons of the cooking liquid.

Transfer the lobsters to a platter and let them cool.

Once cooled, remove the shells from everything but the small claws.

Optionally, reserve the green tomalley if desired.

Coarsely chop the lobster meat and place it in a medium bowl.

Add the unshelled claws, chopped parsley, hard-boiled egg, chopped onion, and chopped pimiento, stirring to combine.

Dissolve the Spanish smoked paprika in the reserved 2 tablespoons of cooking liquid.

In a mortar or mini-processor, mash the garlic, then stir in the paprika mixture.

In a small bowl, whisk together the extra-virgin olive oil, white wine vinegar, salt, and garlic-paprika mixture.

Fold the dressing into the lobster mixture until well combined.

Taste and adjust seasoning if necessary.

Serve the Galician-style lobster salad at room temperature or refrigerate it for at least 2 hours before serving cold.