Preheat the oven to 350 degrees F.
Sautee the onion in the olive oil over medium high heat in a large saute pan. Once the onion begins to soften (about 5 minutes), add the 3 cups of torn/roughly chopped spinach. Cook together until it wilts.
Grease a 3 quart baking dish with butter.
Beat the eggs, milk, pepper, and nutmeg together.
Place a single layer of the bread into the buttered baking dish.
Scatter half of the ham, plus half of the onion and spinach mixture on top. Scatter half of the cheese on top of that.
Place a second layer of bread on top of that.
Scatter the remaining ham, onion, spinach, and cheese on top.
Pour the egg and milk mixture over everything. Firmly press down on it all so that the bread absorbs the liquid.
For best results, let the strata sit covered in the fridge for at least three hours or up to overnight/12 hours. Bake at 350 degrees F for 1 hour and 15 minutes.