Heat the oil in a heavy large skillet over medium heat. Add the pancetta and saute until crisp and golden, about 5 minutes. Using a slotted spoon, transfer the pancetta to a bowl. Add the onion to the pan drippings in the same skillet and saute until translucent, about 4 minutes. Add the spinach and garlic. Saute over medium-low heat until the garlic is tender, about 2 minutes. Stir in 1/2 teaspoon of salt, 1/4 teaspoon of pepper, nutmeg, and the cooked pancetta.
Place half of the bread cubes in a buttered 3-quart baking dish. Sprinkle half of the cheese over the bread, then top with half of the spinach mixture. Repeat layering.
Whisk the milk, eggs, remaining 1/2 teaspoon of salt and 1/4 teaspoon of pepper in a large bowl and pour evenly over the strata. Chill the strata, covered with plastic wrap, at least 2 hours and up to 12 hours.
Preheat the oven to 350 degrees F.
Bake strata uncovered until puffed, golden brown, and cooked through, 40 minutes. Let stand 5 minutes before serving.