Heat oven to 375ºF. Coat 3-quart shallow baking dish with cooking spray.
Put bread in food processor and process to fine crumbs. Set aside.
Heat oil in a large nonstick skillet over medium-high heat. Add onion slices and 1/4 teaspoon of salt. Cover and cook, stirring once or twice, for 5 minutes. Uncover and cook until liquid evaporates, 3 to 5 minutes. Reduce heat to medium, and cook uncovered until onion slices are deeply browned, 15 to 20 minutes more, stirring a few times.
Bring evaporated milk, half-and-half and broth to a boil over medium heat in a small saucepan.
Meanwhile, arrange half of the potato slices in prepared dish, overlapping them slightly. Sprinkle with half of the thyme, half of the black pepper and 1/8 teaspoon of the salt. Top with onions and half of the cheese. Arrange remaining potato slices on top and sprinkle with remaining thyme, black pepper, salt, and cheese. Pour the hot milk mixture over the top.
Cover with foil and bake for 30 minutes. Remove foil, scatter on bread crumbs and coat with cooking spray. Bake until almost all liquid is absorbed and potatoes are tender, 30 to 35 minutes. If necessary to brown top, turn on the broiler and broil until top is golden brown, 1 to 2 minutes.
Tip: Evaporated milk keeps calories in check here, but if you want to splurge, replace it with half-and-half.