Preheat oven to 425°.
Heat a large nonstick skillet over medium-high heat. Add onion slices (keep slices intact); cook 3 minutes on each side or until browned.
Combine milk, salt, thyme, pepper, and eggs in a large bowl, stirring with a whisk. Add the bread cubes and 1/2 cup cheese; toss mixture well. Place the bread mixture in an 8-inch square baking dish coated with cooking spray. Arrange onion slices on top of bread mixture. Sprinkle with 1/4 cup cheese. Bake at 425° 25 minutes or until set and golden.