How to Make It
Preheat the oven to 375°. Bring 4 inches of water to a boil in a large pot. Add the spinach in large handfuls and cook just until wilted, about 2 minutes. Drain the spinach and cool under running water. Drain the spinach again, pressing and squeezing out as much water as possible. Transfer the spinach to a cutting board and coarsely chop it.
In a large, deep skillet, melt 4 tablespoons of the butter. Add the shiitake mushrooms, shallots and thyme and cook over moderate heat, stirring, until softened and just beginning to brown, about 8 minutes. Stir in the flour and cook, stirring, just until the pan looks dry, about 2 minutes. Gradually whisk in the milk and stir until smooth and creamy. Bring to a boil over moderate heat and cook, stirring, until very thick, 2 to 3 minutes. Stir in the spinach and half of the cheese and season with salt and pepper.
Scrape the mixture into a shallow 1 1/2-quart baking dish in an even layer. In a small skillet, melt the remaining 2 tablespoons of butter. Remove from the heat and add the panko and the remaining cheese; season with salt and pepper. Scatter the crumbs over the spinach and bake for about 20 minutes, until the sauce is bubbling and the crumbs are golden. Let stand for 10 minutes before serving.