Diagonally cut baguette crosswise into 3/4-inch-thick slices and brush both sides with butter. Toast on a baking sheet under broiler 3 inches from heat until golden, about 30 seconds on each side.
Preheat oven to 350°F.
Sauté onions in oil in a 12-inch nonstick skillet over moderately high heat, stirring occasionally, until golden. Add ham and sauté, stirring occasionally, until ham is lightly browned.
Whisk eggs in a large bowl and whisk in milk, salt, nutmeg, and pepper to taste. Add toasted bread and toss gently. Transfer bread as saturated to a shallow 3-quart casserole, slightly overlapping slices. Add any remaining egg mixture.
Tuck spinach and ham between slices, reserving a little ham to sprinkle over top. Sprinkle cheese over pudding, lifting slices with a spatula to allow some to fall between them. Sprinkle reserved ham over pudding and bake in middle of oven 45 minutes to 1 hour, or until puffed and edges of bread are golden and custard is set in middle.
