Preheat your oven to 375°F (190°C).

Grease a 9x13-inch baking dish with butter or oil.

Cut brioche bread into 1.5-inch cubes and place in a large mixing bowl.

In a separate bowl, beat together eggs, whole milk, heavy cream, Dijon mustard, thyme, garlic powder, salt, and pepper until well combined.

Pour the custard mixture over the cubed bread, ensuring all pieces are coated. Let sit for 15 minutes.

Sauté the cooked ham in a bit of butter over medium heat until lightly caramelized, about 5-7 minutes.

Layer half of the soaked bread, half of the sautéed ham, and half of the grated cheese in the greased baking dish. Repeat with the remaining ingredients.

Cover and refrigerate overnight or bake immediately.

Bake uncovered for 30-40 minutes, until the top is puffed and golden-brown.

Remove from the oven, let sit for 10-15 minutes, then serve warm.