Leek Bread Pudding

Ingredients:

2 cups ½-inch-thick slices leeks (white and light green parts only)
Kosher salt
4 tablespoons unsalted butter
Freshly ground black pepper
12 cups 1-inch cubes crustless Brioche or Pullman sandwich loaf (I just used whole slice
1 tablespoon finely chopped chives
1 teaspoon thyme leaves (used parsley)
3 large eggs
3 cups whole milk
3 cups heavy cream
Freshly grated nutmeg
1 cup shredded Comté or Emmentaler (I used cheddar and Parmesan)