Place the peas in a large pot and add enough cold water to cover. Bring to a boil. Cover, remove from heat, and set aside for 1 hour.
Meanwhile, heat the oil in a large pot over medium heat. Add the onions, celery, carrots, garlic, and bay leaf. Cook, stirring occasionally, until softened and golden, about 15 minutes. Drain the peas and add them to the vegetables along with the broth. Bring to a boil. Reduce heat, cover, and simmer gently until the peas are softened, about 45 minutes. Remove from heat. Set aside to cool for at least 10 minutes. Remove and discard the bay leaf. Transfer some of the soup to a blender, filling it no more than halfway. Puree until smooth. Repeat with the remaining soup. Return the soup to the pot and place over medium heat until warmed through, about 10 minutes. Season with the salt and pepper. Ladle the soup into individual bowls.
In Advance: Refrigerate the soup for up to 2 days. Warm it over low heat.