Sort and wash the peas. Combine peas, water, oregano, and bay leaves in a medium saucepan. Bring to a boil; cover, reduce heat, and simmer 25 minutes. Stir in 1/4 teaspoon salt; cook 15 minutes or until tender. Drain; discard bay leaves.
Combine the pea mixture, 1/4 teaspoon salt, vinegar, oil, pepper, and garlic in a food processor; process until smooth, scraping sides of bowl occasionally. Stir in olives. Cover and chill 2 hours. Sprinkle with cilantro and arugula, if desired.