How to Make It
Whisk together eggs, half-and-half, and salt until thoroughly blended. Place slices of king cake in a baking dish or similar pan, frosting-side-up, and pour egg mixture in about halfway up the height of the cake. (Since the slices won't be flipped to preserve the frosting, only the bottom half gets soaked and cooked.) Cover and let the slices chill in the refrigerator for 2 hours, then drain the liquid from the pan and let the slices chill and further drain for 1 more hour.
Melt your desired quantity of butter (only you know your soul) in a skillet over medium-low heat and when it has stopped foaming, place the soaked slices frosting-side up in the pan and cook to desired doneness. If desired, to cook the sides more thoroughly, either use tongs to slightly tilt the slices into the butter, or draw it up the sides with a spatula, taking care not to melt the icing. Work in batches if needed, wiping out and re-buttering the skillet as needed. Serve hot.