Preheat your oven to 375°F (190°C) and grease a 9 x 13 baking dish with butter or cooking spray.

Cube the stale brioche bread into 1.5-inch cubes and place in a large bowl.

Whisk together the large eggs, almond milk, non-dairy creamer or heavy cream, Dijon mustard, thyme, garlic powder, salt, and pepper until smooth.

Pour the custard over the cubed bread and mix gently until each piece is coated. Let sit for 15 minutes.

Sauté the cooked ham in a non-stick skillet over medium heat until lightly caramelized, about 5-7 minutes.

In the greased baking dish, layer half of the soaked bread mixture, half of the sautéed ham, and half of the grated cheese.

Repeat the layering process with the remaining soaked bread, ham, and cheese.

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

Let the dish rest for 10-15 minutes before slicing.

Slice into squares and serve warm with fresh fruit or a tossed salad.