Melt the butter in a heavy-bottomed saucepan over medium heat. Add the chopped shallots and cook until soft and translucent, about 3 minutes, without browning.
Pour in the water and add the fresh peas. Season with salt and pepper, then increase the heat to medium-high and bring the mixture to a boil. Once boiling, reduce the heat to low, cover, and let it simmer gently until the peas are tender, about 12 to 18 minutes.
Carefully puree the soup in batches using a blender or food processor until smooth. Strain the puree back into the saucepan for a silky texture.
Stir in the whipping cream if using, gently reheat the soup, and adjust seasoning with additional salt and pepper. Serve warm.
