Preheat the oven to 325°F. Generously coat a 9x13-inch ceramic baking dish with unsalted butter or vegetable oil spray.

Carefully trim the crusts from the slices of white bread and discard them (the crusts inhibit uniform liquid absorption).

Using a sharp serrated knife, cut the soft, crustless bread into uniform 1-inch cubes. Place the cubes into a large mixing bowl.

In a separate, large glass or ceramic mixing bowl, vigorously whisk together the large eggs and whole milk until completely unified and pale yellow.

Whisk the chopped garlic chives, prepared coarse mustard, kosher salt, and several dashes of hot pepper sauce into the egg mixture to establish a deep, savory flavor profile.

Pour the seasoned egg custard directly over the cubed white bread in the large mixing bowl.

Add the freshly shredded sharp cheddar cheese and diced green onions.

Using a large wooden spoon or rubber spatula, gently fold the mixture together until the bread cubes are entirely saturated and have absorbed a significant portion of the liquid custard.

Pour the saturated mixture evenly into the prepared baking dish, ensuring the cheese and bread are uniformly distributed. (For a make-ahead option, the casserole can be tightly covered and refrigerated overnight at this stage).

Bake in the preheated 325°F oven for approximately 1 hour. The casserole is finished when the center is just barely set and puffed, and the edges have turned a deep, caramelized golden brown.

Allow the dish to rest for 10 minutes before slicing to ensure the custard structure sets perfectly for serving.