Place the thawed spinach into a colander. Press on the spinach to squeeze out as much liquid as possible.
Sauté the onion in the butter over medium heat, stirring occasionally, until onion is soft and transparent, around 5 minutes. Add ½ teaspoon of the salt, ¼ teaspoon of the black pepper, and all the nutmeg. Continue to cook for one minute, stirring to combine. Add spinach (it will be clumpy, break it up with your cooking spatula). Remove from heat.
Scatter one third of bread cubes in a buttered 3-quart oven-to-table baking dish and top evenly with one third of spinach mixture. Sprinkle with one third of the shredded cheese. Repeat layering twice (ending with cheese).
Whisk eggs in large bowl. Add mustard, milk and remaining 1/2 teaspoon salt and 1/4 teaspoon pepper. Pour custard mixture evenly over strata. Chill the strata, covered with plastic wrap, 8-10 hours, or overnight.
Take strata out of fridge and leave at room temperature for 30 minutes. Preheat oven to 350°F.
Put the strata at the center of the oven and bake uncovered until puffy, golden, and baked through, about one hour. Allow strata 5 minutes resting time before serving.