Preheat your oven to 350°F (175°C).

In a large mixing bowl, cube your hearty bread into bite-sized pieces. Add in the eggs, cream, and prepared béchamel sauce, stirring until every piece is well-coated. Allow the mixture to sit for 15 minutes.

Grease a 9x13 inch casserole dish well with butter or cooking spray. Layer half of the bread mixture, followed by half of the Gruyere cheese and smoked ham.

Repeat the layering process with the remaining mixture, cheese, and ham. Press down gently to ensure the layers are compact yet still airy.

Crack a couple of eggs on top. Sprinkle fresh thyme and black pepper over the eggs.

Place the casserole dish in the preheated oven and bake for 38-40 minutes.

Once baked, remove the casserole and let it rest for 5-10 minutes before slicing.