How to Make It
Heat the oven to 325°. Butter a 9-by-13-inch baking dish or a gratin dish of similar size. In a large nonstick frying pan, melt the butter over moderately low heat. Add the onion and celery; cook, stirring occasionally, until starting to soften, about 3 minutes. Increase the heat to moderately high. Add the mushrooms and thyme and cook until the mushrooms start to brown, about 5 minutes. Remove the pan from the heat. Stir in the bread cubes, 3/4 teaspoon of the salt, and 1/4 teaspoon of the pepper. Transfer the mixture to the prepared baking dish.
Stir together the broth, eggs, and half-and-half. Pour the mixture evenly over the mushrooms and bread. Put the dish in the lower third of the oven and bake for 25 minutes.
Meanwhile, heat the oil in the frying pan over moderate heat. Sprinkle the remaining 1/4 teaspoon each salt and pepper over the pork chops. Add the chops to the pan and brown, about 3 minutes per side. Remove the chops from the pan. Remove the bread pudding from the oven after it bakes for 25 minutes and set the pork chops directly on top. Return to the oven and cook until the meat is done and the pudding is just set, 10 to 15 minutes longer.