The potato boats and eggs in this brunch dish can be made completely ahead of time. Just reheat and serve with the toppings of your choice.
The night before serving — make the potatoes:
Preheat the oven to 400 degrees F.
Prick each potato a few times with a fork, then rub the potato skins lightly with olive oil. Place the potatoes on a baking sheet and cook for 45 minutes to 1 hour, until the potatoes are fully cooked and a knife inserted through the potato meets with no resistance. Transfer the potatoes to a rack and let cool until you can touch them without burning yourself. Slice the potatoes in half lengthwise, then scoop out the interior of each half to make a boat, leaving about 1/4 to 1/2 inch of potato attached to the skin. Place the boats on a clean baking sheet or in a casserole dish. (Save the scooped-out potato to make mashed potatoes or to reheat with butter or sour cream as a side dish.) Lightly whisk the eggs, milk and salt together in a bowl. Melt the butter in a large cast iron or nonstick skillet over medium low heat, swirling until it completely coats the bottom of the pan. Pour in the eggs and cook undisturbed for about 2 minutes, until a layer of cooked egg forms across the bottom of the pan. Push the edges of the cooked egg up with a silicone spatula to form soft curds of cooked egg and let the remaining uncooked egg come into contact with the pan. Cook for 1-2 minutes more, then sprinkle the cheese over the egg. Gently fold the cheese into the cooked egg so it melts. Divide the cheesy eggs between the potato boats. Cool to room temperature, then cover the boats with foil or plastic wrap and refrigerate overnight.
The next morning — reheat and serve:Reheat the potatoes in a 350-degree oven for about 15 minutes until warmed through. Place toppings into bowls and arrange buffet-style on a table. Let guests top their own potato boats with their favorite toppings and eat immediately!