In a 2-quart baking dish, combine bread, apple, and cheese.
In a bowl, whisk together eggs, milk, half-and-half, maple syrup, salt, and thyme, beating until frothy. Pour over bread and stir a bit to ensure even coverage.
Cover with plastic wrap and place in the refrigerator for at least 2 hours, or overnight.
When ready to bake, preheat oven to 375°F and remove pudding from the refrigerator to bring up to room temperature.
Bake for 1 hour 30 minutes, until nicely browned on top. It will puff up while baking but deflate as it cools. Serve warm.