Heat the oil in a saucepan on medium flame. Sauté the onions until translucent, about 5 minutes. Do not let the onions brown.
Add the first pound of peas, the water, the first ¼ cup of mint, the basil, and the salt. Bring to a boil, lower the heat, and simmer 10 minutes. (If you are using only frozen peas, simmer 20 minutes.)
Stir in the frozen peas and the remaining fresh herbs. Cook just until the second batch of peas are tender and hot.
Puree the soup using an immersion blender, or in batches in a regular blender.
Serve cold, or hot, with dollops of goat cheese or swirls of sour cream and fresh peas or snow peas. Decorate with fresh mint and basil leaves.