Melt the butter in a heavy large saucepan over medium heat. Add the shallots and fennel. Season with 1/2 teaspoon of the salt and 1/4 the teaspoon pepper. Cover the saucepan and cook until almost tender, stirring occasionally, 6 to 7 minutes. Add the lettuce and toss until wilted, 1 to 2 minutes. Mix in the peas, broth, 1 cup water and fennel seeds. Bring the soup to a boil. Cover; reduce the heat to medium-low and simmer until the vegetables are just tender, 5 to 6 minutes.
In a blender, blend the soup, 1 cup at a time, until smooth. Pour the soup back into the saucepan and keep warm over low heat. Season with the remaining 1/2 teaspoon salt and 1/4 teaspoon pepper. Thin out the soup by adding 1 tablespoon of extra broth at a time, if needed.
Ladle the soup into bowls and serve.
When blending hot liquids, first let cool for 5 minutes or so, then transfer to a blender, filling only halfway. Put the lid on, leaving one corner open; this will prevent the vacuum effect that creates heat explosions. Cover the lid with a kitchen towel to catch splatters and pulse until smooth.
Recipe courtesy of Giada De Laurentiis