Clean and slice the leeks into half-inch rounds. Soak in cold water for 10 minutes to remove dirt, then drain and pat dry.

In a dry skillet over medium heat, sauté leeks with a pinch of salt and pepper for 20-30 minutes until soft and caramelized.

Preheat oven to 350°F (175°C). Cut bread into cubes, spread on a baking sheet, and toast for about 20 minutes until golden.

In a large bowl, whisk together eggs, milk, half-and-half, Dijon mustard, salt, white pepper, and herbs until smooth.

Grease a 9x13-inch baking dish with butter. Layer half of the Gruyère cheese at the bottom.

Mix sautéed leeks with toasted bread cubes. Layer this mixture over the cheese and pour custard evenly on top.

Let the mixture rest for 10 minutes at room temperature.

Bake in the oven at 350°F (175°C) for about 1½ hours until puffed and golden brown on top.