Cook your peas and lentils, in the water and broth in a large pot over medium heat for 90 minutes to two hours, or until soft. Do not drain. Transfer to a large bowl and set aside.
In a saute pan, heat the oil. When heated, saute the onion, carrot, and celery with the bay leaves until soft. Make sure you remove the bay leaves.
Puree the vegetables in a blender until smooth. Move to a large pot. Puree the peas and lentils in batches in the blender until smooth. Add that to the vegetable puree, and cook over medium low heat until warm. Serve in bowls.