How to Make It
Melt 4 tablespoons of the butter in a medium skillet. Add the shallot and a pinch of salt, cover and cook over low heat until softened, about 2 minutes. Add the chopped stems and cook over moderately low heat until the liquid has evaporated but the mushrooms are still white, about 5 minutes. Add the cream and lemon juice, cover partially and cook over moderate heat until slightly thickened, about 5 minutes.
Pour the water into a large skillet. Add the remaining 2 tablespoons of butter and a generous pinch of salt and bring to a boil. Add the mushroom caps, stemmed side up, cover and cook over moderate heat until tender, about 5 minutes. Uncover and cook, stirring occasionally, until the liquid has evaporated and the caps are browned, about 5 minutes longer. Turn the caps stemmed side down to drain any remaining liquid.
Transfer the caps to a platter and spoon in the filling. Scatter the chives on top. Serve warm or at room temperature.