Trim leeks to use only white and light green parts, rinse, slice and sauté in a skillet with oil, salt, and pepper for about 30 minutes.

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

Whisk eggs, milk, half and half, Dijon mustard, salt, white pepper, and nutmeg in a mixing bowl; stir in chopped herbs.

Grease a baking dish and layer half of the toasted bread, all of the sautéed leeks, and half of the grated Gruyère.

Repeat layers with remaining bread and cheese, then pour custard mixture over layers and let rest for 10 minutes.

Bake in the oven for 1.5 hours until puffed and golden. Test doneness with a knife in the center.

Let the pudding rest in the oven for 15 to 20 minutes before serving.