1. Trim and discard the hairy ends and the tough dark green outer layers of the leeks. Cut the leeks in half lengthwise. Lay one half flat and, starting at the light end, slice the leeks ½ inch thick on an extreme bias, stopping when the leeks become dark green. Discard the dark green ends and repeat, slicing the rest of the leeks in the same way. Wash and dry the leek slices thoroughly and separate the layers.

2. Heat the butter in a large sauté pan over medium heat until it just melts. Add the leeks, season with ½ teaspoon of the salt, and sauté the leeks for about 5 minutes, until they're soft and translucent, stirring often so they don't brown. (Lower the heat if the leeks begin to brown before they are soft.) Add the spinach, season it with % teaspoon of the remaining salt, and gently fold the spinach in with the leeks so it wilts and fits in the pan. Continue to cook the spinach, stirring often, until all the water released from the spinach during cooking has evaporated, about 5 minutes. Transfer the vegetables to a plate and set aside to cool to room temperature.

3. Adjust an oven rack to the middle position and preheat the oven to 300 'F. Whisk the eggs in a medium bowl to break up the yolks. Add the milk, 1 tablespoon of the thyme leaves, and the remaining tablespoon salt and whisk to com bine the ingredients.

4. Lay the croissant bottoms, cut side up, in the bottom of a 9 x 13-inch casserole dish, trimming them as necessary to make them fit in a single layer like pieces of a puzzle. Pour 2 cups of the custard over the surface of the croissants, pouring it over the entire surface, not dumping it in one place, and press gently on the croissants with your fingers to help them absorb the liquid. Sprinkle two-thirds (4 ounces) of the Comté over the croissants and pour 2 cups of the remaining custard over the cheese, pouring it over the entire surface. Lay the ham strips in an even layer and scatter the spinach and leeks over the ham, spreading them in an even layer (the best way to do this is with your hands). Lay the croissant tops, cut sides down, on top of the filling, again cutting them as needed so they fit in the dish. Pour the remaining custard over the entire surface of the croissants.


5. Combine the remaining 2 ounces Comté and the Parmigiano in a small bowl and sprinkle it over the top of the croissants. Press down on the croissants to nestle them tightly in the dish and to push out any air bubbles. Scatter the butter pieces and sprinkle the remaining thyme leaves over the top of the bread pudding.

6. Put the bread pudding on a baking sheet and bake for 1 hour 10 minutes to 1 hour 20 minutes, until the top is golden brown and an instant-read thermometer inserted into the center registers 165°F, rotating the baking sheer from front to back halfway through the cooking time so the bread pudding browns evenly. Remove the bread pudding from the oven and set it aside to rest for 45 minutes to 1 hour before serving.