Brush the lining of your baking vessel with butter (use a loaf pan or 8 fluid-ounce mugs or ramekins for individual servings). Layer the bread in the cooking vessels.

Prepare the custard mixture by combining the eggs, heavy cream, vanilla, salt and 1/3 cup brown sugar, mixing well to dissolve the sugar.

Divide the prepared custard among each baking vessel. Pour it over the bread so the bread is submerged in custard. Sprinkle diced apple on the top of each bread pudding. In a bowl, mix the granulated sugar, remaining brown sugar, and cinnamon. Use a sifter or fine mesh strainer to sprinkle the cinnamon sugar over the top of each vessel, then place the baking dishes in the refrigerator to rest for 1 hour to allow the bread to soak up the custard.

Preheat the oven to 325 degrees F.

Make apple cider glaze by pouring the apple cider into a saucepan and bringing it to a simmer over moderate heat. Leave uncovered. Reduce to soft ball consistency and a temperature of 235 degrees F. Remove from heat and whisk in the heavy cream while still hot. Adjust consistency as desired with additional cream or water. Glaze will thicken slightly as it cools.

Place the baking vessels into a larger oven-safe dish and fill with hot water 130 to 140 degrees F, leaving ¼ inch headspace. Transfer to preheated oven to bake until the custard is set or the bread pudding reaches an internal temperature of 160 degrees F and the bread on top begins to brown, approximately 40 minutes. Drizzle apple cider glaze over each dish and serve warm.