Spray a 9x13-inch baking dish with non-stick cooking spray.
MAKE EGG MIXTURE:
In a large bowl, whisk the eggs and yolks until smooth.
Add the milk, heavy cream, and oil and whisk until combined.
Whisk in rosemary, salt, pepper, and thyme.
ASSEMBLE:
In the prepared baking dish, arrange the bread in a single layer.
Sprinkle about ¾ of the cheese and ¾ of the bacon bits over the bread.
Pour the egg mixture over the bread and press the bread down slightly into the egg mixture to make sure all of it is saturated.
Sprinkle the remaining cheese and bacon bits over the top.
BAKE:
Bake for 45 minutes, until set and golden.
Once baked, remove from the oven and serve immediately.
Notes
To prevent the bread pudding from getting too crisp on top, you may bake it with a water bath.
Adjust the racks to where one is below the middle rack.
Fill a baking dish with 1” of water and place it on the bottom rack after you have set the bread pudding into the oven.
If the top of the bread pudding starts to burn before the baking time is up, loosely cover it with tin foil. This will prevent it from burning while it finishes baking.