Step 1

Butter a 9-inch x 13-inch baking pan. Set aside.

Step 2

Prepare the Day Before: Heat the butter in a 12-inch skillet over medium heat until melted and lightly bubbling. Add the shallots and pinch of salt and sauté, stirring frequently, until softened, 3 to 4 minutes. Add the chard stems and cook, stirring frequently, for an additional 4 to 5 minutes. Add the chopped chard greens and another pinch of salt, and sauté, flipping the greens with tongs, until wilted and tender, about 5 minutes. Remove from the heat and season to taste with salt and freshly ground black pepper. Cool to room temperature before using.

Step 3

In a large bowl, whisk together the eggs, whole milk, Dijon mustard, nutmeg, and kosher salt. Distribute half of the bread cubes in the buttered dish, top with half of the cooked green mixture, and sprinkle with half of the shredded cheese. Repeat with the remaining bread, greens, and cheese to create two layers. Pour the egg custard evenly over the top. Cover tightly with foil and refrigerate overnight (or a minimum of 1 hour, if baking the day).

Step 4

Bake the Strata: Remove the strata from the fridge and allow to sit at room temperature as the oven preheats or at least 30 minutes. It will have thickened considerably overnight.

Step 5

Preheat oven to 350°F (176°C) with a rack in the center position. Bake uncovered for 55 to 65 minutes or until puffed, golden, and cooked through. Allow the strata to cool on a rack for 5 to 10 minutes before serving.

Step 6

Leftovers can be covered and refrigerated for 3 to 4 days. Serve cold, at room temperature, or reheat in short intervals in the microwave or in a 325°F (162°C) oven.