Step 1 Heat 2 tablespoons butter in a large skillet over low heat until it turns a nut brown color. Skim off any foam and set aside.
Step 2 Wash the spinach and remove stems. Pat dry on paper towels. Clean the mushrooms with a damp towel. Peel and trim the mushrooms, reserving trimmings for the sauce. Slice the mushrooms as thin as possible.
Step 3Lightly saute the mushrooms in the reserved brown butter. Season with one-half teaspoon salt and one-eighth teaspoon pepper. Allow to cool enough to handle.
Step 4Melt the remaining 2 tablespoons butter in a large skillet, add the spinach and cook until the spinach is wilted, about 2 minutes. Season with one-half teaspoon salt and one-eighth teaspoon pepper and keep warm. Drain off excess liquid from the spinach.
Step 5Put the heavy cream and mushroom trimmings in a small saucepan over medium-high heat. Let reduce by one-third, and puree in a blender until smooth. Season to taste with salt and pepper. Set aside and keep warm.
Step 6To assemble the gratin, place the wilted spinach in the bottom of a 9-inch gratin dish. Arrange the mushroom slices in a spiral pattern, the slices overlapping each other, on top of the spinach. Spoon over the mushroom cream. Put the gratin under the broiler 4 to 5 minutes until golden brown on top.