Grease an approximately 11-by-7-inch (or 2-quart casserole) glass baking dish. Wilt spinach by putting in steamer over boiling water for 2-3 minutes, or sautéing in 1-2 tablespoons of olive oil until wilted. In a medium bowl, whisk together eggs, egg whites and milk. Add mustard, pepper and rosemary, whisking to combine. (The more you whisk, the lighter the custard.) In a large bowl, toss bread, spinach, roasted red peppers and ham. Add the custard and toss well to coat. Transfer to the prepared baking dish and push down to compact. Cover with foil. Bake at 375 degrees until the custard has set, 40 to 45 minutes. Uncover, sprinkle with cheese and continue baking until the pudding is puffed and golden on top, 15 to 20 minutes more. Remove from oven and cool for 15 to 20 minutes before serving. Serve with Gruyere Cheese Sauce drizzled on top of wedge of bread pudding.