Add the scallions and cook, stirring occasionally, until they begin to soften, 2 to 3 minutes (don’t let them brown). Increase the heat to medium, add the peas and lettuce and continue to cook, tossing with tongs, until the lettuce begins to wilt, 2 minutes more. Add the broth and a pinch of salt and pepper. Stir well and bring to a simmer.
Melt the butter in a medium skillet over medium heat. Add about 1 tablespoon olive oil and the sliced scallions. Cook for a few minutes, or until the scallions are softened. Meanwhile, slice the lettuce leaves, saving a few tender inner leaves to add at the end.
Raise the heat under the pan and boil the juices until reduced by half. Add the cream or crème fraîche and petits pois and boil for 1 min until heated through. Arrange lettuces in a serving dish and pour over the pea-and-cream sauce.