How to Make It
Bring the water to a boil in a large saucepan. Salt the water, then add the peas and bring the water back to a boil. Cook over moderate heat until very tender, about 20 minutes. Drain the peas, reserving the cooking liquid. Set aside 1/4 cup of peas.
In a food processor, combine the remaining peas with 1/4 cup of the olive oil and 1/4 cup of the reserved cooking liquid and puree until smooth. Work the puree through a fine sieve into a large bowl. Discard the contents of the sieve. Stir in about 4 cups of the cooking liquid and season with salt and pepper; add more cooking liquid if necessary to make a nice, creamy soup. Refrigerate the soup until cold, at least 2 hours.
In a large skillet, melt the butter in the vegetable oil. Add the diced bread and brown the cubes on all sides over moderately high heat, 3 to 5 minutes. Drain the croutons on paper towels.
Ladle the cold soup into bowls and garnish each with a few of the croutons and reserved peas. Drizzle with olive oil, sprinkle with pepper and serve.