Preparation

• Melt the butter in a large (12-inch) skillet over medium-high heat. Add the asparagus, sprinkle with 1/2 tsp. each salt and pepper, and cook, stirring occasionally, until the spears start to brown and soften, about 3 minutes. Add the mushrooms and scallion whites and cook, stirring occasionally, until the mushrooms soften and cook through, about 2 minutes. Remove from the heat and let cool for a couple of minutes.
• Butter a 9×13-inch baking dish. Whisk the eggs with the milk and 1/2 tsp. each salt and pepper. Spread half the bread in a single layer on the bottom of the baking dish. Top with half the egg mixture and then cover with half the ham, cheese, and asparagus mixture, and sprinkle with half the scallion greens. Repeat with the remaining bread, custard, ham, cheese, asparagus mixture, and scallions. Cover with plastic wrap, pressing down so the bread is completely submerged in the egg mixture, and refrigerate for at least 4 hours and up to 2 days before baking.
• Put a rack in the center of the oven and heat the oven to 350°F. Let the strata sit at room temperature while the oven heats. Bake until the custard sets and the top browns, about 30 minutes. Loosely cover with foil and bake for another 20 minutes. Let cool for 10 minutes, cut into square pieces, and serve.