1. Preheat oven to 350 degrees.

2. Fill a large bowl with water and add leek slices. Swirl leeks so that any dirt falls to the bottom of the bowl. Heat a medium skillet over medium-high heat; using your hands, lift leeks out of water and transfer to skillet. Cook, stirring often, until leeks begin to soften, about 5 minutes.

3. Reduce heat to medium-low; continue cooking until leeks release their liquid. Add butter to skillet and stir to emulsify; season with pepper. Cut a parchment paper round the same size as the skillet with a 1-inch hole in the center and set round in skillet. Cook leeks, stirring every 10 minutes, until very soft, 30 to 35 minutes. If the butter breaks or looks oily, stir in a tablespoon water to re-emulsify. Remove and discard parchment lid.

4. Meanwhile, spread bread cubes on a baking sheet and toast in oven for about 20 minutes, rotating pan about halfway through, until dry and lightly toasted. Transfer to a large bowl. Add leeks to bread; toss to combine. Add chives and thyme.

5. In another large bowl, lightly whisk eggs. Add milk, cream, a generous pinch of salt, pepper, and a pinch of nutmeg; whisk to combine. Set custard mixture aside.

6. Sprinkle 1/4 cup cheese in the bottom of a 9-by-13-inch baking dish. Spread half of the leek mixture in baking dish and sprinkle with another 1/4 cup cheese. Repeat process with remaining leek mixture and 1/4 cup cheese. Pour enough of the custard mixture over leek mixture and press gently on bread so it soaks up the custard. Let soak for 15 minutes.

7. Pour remaining custard over leek mixture. Sprinkle with remaining 1/4 cup cheese and season with salt. Transfer to oven and bake until pudding is set and top is brown and bubbling, about 1 1/2 hours. Serve.